By Maggie Fox, CNN

(CNN) -- A vaccine kit sent to the wrong state. A hospital system in California expecting to get powdered vaccines instead of frozen vials. And tens of thousands of people expect to get vaccinated in the coming weeks, when in reality they are going to have to wait for months.

The rollout of the first coronavirus vaccine is already messy, and it has only been authorized since late Friday night.

The US Food and Drug Administration granted emergency use authorization to Pfizer and BioNTech's vaccine Friday, and it's widely expected to grant EUA to Moderna's similar vaccine next week. Vaccinations are expected to begin Monday.

The federal government's Operation Warp Speed has been gearing up and holding news conferences headlined by generals promising a military-style rollout. But jokes about military precision aside, experts are already expecting a lot of confusion, a fair amount of fear and more than a little outrage.

"The public has to be cognizant that there is going to be unfairness or error or sometimes just stupidity," said Juliette Kayyem, a security specialist at Harvard's Kennedy School of Government and former assistant secretary for intergovernmental affairs at the Department of Homeland Security during the Obama administration.

Here are some of the problems the US public can expect to see with any mass vaccination effort.

People will have to wait

It's clear there will not be enough vaccines for everyone who wants one right away. Pfizer is only expected to be able to supply 2.9 million doses in the first few days and only up to 6.4 million doses by December 19, according to Operation Warp Speed, the government's vaccine effort. Both Pfizer and Moderna together can only supply, at the most, 40 million doses by the end of the month.

Vaccine advisers have already broken down priority groups into subgroups, and have only designated the very, very first people to get vaccines. Those in this 1a group designated by the Advisory Committee on Immunization Practices will include frontline health care workers and people in long-term care homes.

But even that small group already outnumbers the vaccine supply. It's about 24 million people, and 40 million doses will only cover 20 million. Hospitals are planning to triage.

"I think we anticipate that we will not have enough for everybody at once. It's not going to be a one and done event," Dr. Marci Drees, chief infection prevention officer and hospital epidemiologist for Delaware-based ChristianaCare, told CNN. "We don't know exactly how many vaccines we'll get."

Operation Warp Speed chief adviser Moncef Slaoui has projected Pfizer and Moderna together can make and deliver 60 million to 70 million vaccines in January, and hopes two other vaccines makers, AstraZeneca and Johnson & Johnson, will join the mix of authorized vaccines in the coming months.

"We can immunize 20 million in December, 30 million in January, 50 million in February," Slaoui said at the White House Tuesday. But he doesn't project having vaccinated the full population until June.

And that's assuming nothing goes wrong with manufacturing. Moderna and Pfizer each say they can make up to a billion doses by the end of 2021, but Moderna says it might be half that -- it's never made a product for sale before -- and Pfizer has already severely adjusted its timeline for vaccine delivery after unspecified manufacturing problems.

Distribution may seem unfair

ACIP is the main group advising the US Centers for Disease Control and Prevention, which in turn offers guidance to states. State and local authorities make their own decisions on who gets vaccinated, and when. The decision to vaccinate health care workers, nursing home residents and patients in rehabilitation facilities first was an easy one --people want doctors, nurses, technicians and others to be able to safely care for everyone, and long-term care facility residents have made up 40% of deaths so far.

But it's going to get sticky after that.

A big chunk of Americans fall into one high-risk group or another -- especially since obesity raises the risk of severe disease, and more than 40% of Americans are obese. People over 65, people with diabetes, people with kidney disease, ethnic minorities, people with other chronic conditions -- it will be hard to choose just a few of these groups to go next.

And what about essential workers? The groups advising ACIP, including Johns Hopkins University and the National Academies of Science, Engineering and Medicine, say it would be prudent to vaccinate people who work in food production, emergency workers and utility workers ahead of the general population.

ACIP member Dr. Robert Atmar, a professor of infectious diseases at Baylor College of Medicine, said ACIP will likely put essential workers into group 1b. "That would include teachers, people in law enforcement, firefighters and a variety of other groups, and then 1c would be persons with underlying conditions who had higher risk of developing complications or dying should they get Covid-19 and that would include persons over the age of 65," he said.

But even that could seem unfair, Kayyem said.

"There are a lot of people who are 64 years and 300 days who will say, 'in just a couple of weeks I could be in the next pool,'" Kayyem said. "It is going to seem somewhat unfeeling."

Organizations representing patients with various chronic conditions have started lobbying to ensure their particular patient populations of interest are included in the early target groups.

"There is no doubt that our country must give first access to populations most at risk for the worst of Covid-19's complications -- including 34 million Americans living with diabetes," American Diabetes Association CEO Tracey Brown argued in a commentary on CNN.com.

"In discussion of who should qualify for Phase 1b access to a vaccine, ACIP thus far has discussed individuals with high-risk medical conditions, namely cancer, chronic kidney disease, chronic obstructive pulmonary disease (COPD), immunocompromised state from solid organ transplant, obesity, a serious heart condition, sickle cell disease, and type 2 diabetes," the Muscular Dystrophy Association wrote in a letter to ACIP.

"MDA strongly believes that individuals living with a neuromuscular disease should be included in Phase 1b of vaccination administration due to the complexity of the multisystem impact of neuromuscular diseases that results in co-morbidities that cause a high risk for adverse Covid outcomes."

Kayyem also envisions a rural versus urban divide. "It is very likely you are going to want the Pfizer vaccine to go to urban areas because it has to be frozen. That easier to do in urban areas than in rural areas," she said. For instance, the head of the Healthcare Association of Hawaii told CNN last month that not a single hospital in Hawaii had a freezer that can stay cold enough to store Pfizer's coronavirus vaccine and the state may not have enough access to dry ice to make proper use of the company's distribution boxes.

And because the vaccines must be stored carefully and require two doses, some local decisions may be made to make efficient use of the vaccines. Some counties, for instance, may decide to vaccinate all staff and residents of nursing homes -- even those who do not fall into designated priority groups. Others may offer vaccines to relatives so they can visit and help care for their loved ones. Some hospitals may opt to vaccinate patients along with staff to make good use of their vaccine allocations.

There will be side effects

Susan Froehlich of Dallas was pretty sure she got the real vaccine and not a placebo when she volunteered to take part in a clinical trial testing Moderna's vaccine. "About 12 hours after I got the booster, it was 2:30 in the morning and I woke up with a terrible stomach ache and a headache and it was like I was at the beginning stages of a bad flu," Froehlich told CNN's coronavirus town hall last week

"It was like every part of my body was hurting for about four hours," Froehlich added. She felt better after taking naproxen.

It's not unexpected. Slaoui has said up to 15% of Pfizer and Moderna vaccine trial participants have "quite noticeable side effects" including nausea, body aches, headaches and chills.

"I think those side effects are somewhat common," Slaoui told CNN earlier this month. They resolve quickly, but CDC and other officials are worried they might scare some people away from getting a second dose of the vaccine and are preparing educational materials to let people know the symptoms are a sign the vaccine is working to rev up the body's immune response and are harmless.

Hospitals and the military are also planning around the possibility of having staff out sick after getting the shots. "You don't want to vaccinate everybody on the same day," Drees said. Instead, several hospitals have said they'll stagger vaccinations just in case significant numbers of staff miss a few hours or even a day of work after getting the shot.

There will be vaccine scares

Pfizer's vaccine has already had its first scare, with reports of two allergic reactions during the rollout in Britain. Both patients recovered, but the incidents were enough to delay the US EUA by several hours while the FDA hashed out possible label changes for the vaccine.

In September, AstraZeneca paused its coronavirus vaccine trials because of a severe adverse event in a volunteer. The company later said one volunteer had "an undiagnosed case of multiple sclerosis" and a second volunteer had "an unexplained illness." An internal company document pointed to a rare neurological condition called transverse myelitis. The trials restarted in Britain and elsewhere a few weeks later, but it wasn't until October 23 that the FDA allowed the trial to resume in the US after determining that the case was unrelated to the vaccine.

AstraZeneca went through another scare when a volunteer in a trial in Brazil died, but it turned out the volunteer had been given a placebo and had died of Covid-19.

"One of the groups that is queued up to get vaccines early are the residents of long term care facilities," said Dr. Nancy Messonnier, who heads the CDC's respiratory diseases and immunizations branch.

"They are getting vaccine early because they're among the most fragile -- 40% of deaths have been in those populations. They are medically fragile," Messonnier said in an interview with the Aspen Institute Monday.

"If we vaccinate in a nursing home on Monday, somebody dies on Wednesday, it will be a terrible tragedy. It may, but it's likely not related to the vaccine. So I hope that people will try to not jump to conclusions."

Such scares are certain to become more common as more and more people get vaccinated. The CDC plans to actively ask people about symptoms using a text-messaging app called V-Safe. At the same time, social media may be filled with stories of people who suffer illnesses or accidents and who link them to the vaccine -- whether they are directly related or not.

Drees said her hospital system will be ready to hear of these from workers who get vaccinated and is preparing an education campaign to help deal with it. "We are very comfortable with the science behind this vaccine," she said.

There will be mistakes

Colorado saw a snafu with its very first rehearsal. A test shipment of a vaccine ancillary kit containing syringes, alcohol and other supplies got shipped to another state by mistake. "This error in shipment was due to a label printing error with the manufacturer. The manufacturer has corrected the problem, but Colorado will not be receiving a second test shipment of the 'mock' ancillary kit," the state said in a statement earlier this month.

One hospital system in California prepared its staff to receive vaccine in powdered form from Pfizer. Pfizer's vaccine is, in fact, shipped as a frozen fluid that must be diluted.

"One of the challenges that has not gotten a lot of attention is that we have not factored in space in our timeline to do a lot of hands-on training with the people who will be administering these vaccines," said Dr. Kelly Moore, associate director of the Immunization Action Coalition, which is supporting frontline workers who will administer Covid-19 vaccinations.

Such mistakes can make for a rough rollout, said Mike Osterholm, head of the Center for Infectious Disease Research and Policy at the University of Minnesota and an adviser to President-elect Joe Biden's transition team.

"Having a vaccine means nothing if it doesn't result in a vaccination. For that to happen, the vaccine has to travel the last mile to arrive on time, at the right temperature and where it will end up in the arm of the intended vaccinee," Osterholm said.

There are many opportunities for mistakes to be made, Kayyem said.

"Any supply chain in which demand exceeds supply is going to be complicated because you are making allocation decisions all the time. You are making them across a country that is geographically dispersed, that is divided, and that is in the middle of a pandemic," Kayyem said.

Vaccines that must be kept frozen at ultra-cold temperatures may thaw out and have to be thrown away. Vaccines may get sent to the wrong destination. A nurse may vigorously shake a precious vial of Pfizer vaccine -- the package insert says that can ruin it, and instead says the vial should be inverted gently a few times to mix the contents. People will forget to come back for their second doses.

"There will be course corrections and someone, sometimes, is just going to do something stupid," Kayyem said.