In my opinion, here are the main problems with routine, global vaccination of the very young and very elderly:
Corruption can occur in any area that deals with vaccination, in the financing, the research, the ethics of the company, the practices of the company, the production of the product, and in the distribution of the product, and in the marketing of the product. Any area can become corrupted by the pressures of stockholders, traders, and people just getting greedy or just trying to make a living and looking the other way to do it. Or there are people who tend to think that everything must be OK because everyone else is doing it.
Where ever there is a lot of money to be made, corruption is a possibility, and some might say that because it is a part of human nature to focus on money -- a probability, -- which is why in all functioning social systems we have a form of checks and balances, and several forms of accountability and consequences.
Where are the products made? Who is making them? What laws are in effect to control these processes and people? Are the standards enough to prevent most mistakes?
Until you test the product on a group of people for an entire life-cycle, you really don't know the long-term implications. Until you test an entire population of people, you won't know how the effect of changing their immunity will affect the group. This is impractical and so isn't done.
Limits to Research in Real Life
You can test the product given individually, but seldom is a product tested with other products that people are given or are taking at the same time. I think the MMR is a problem because the three viruses are given together, and then often other vaccinations are given with this one, so that a child can get 6 or more diseases injected into them all in one day...causing their immune systems to over-react. My son got a mild case of lead poisoning during the time he was vaccinated, which I think is why he got Autism and I didn't. However, lead poisoning is extremely difficult to prevent in certain situations, and very dangerous in children under age three because of how the body develops.
Auto-immunity is when the immune system becomes unable to distinguish between "self" and "not-self."
Auto-immunity is a real problem when there are dietary deficiencies that prevent the immune system from calming itself down after exposure to a disease.
Immunizations need preservation to keep from spoiling. Refrigeration isn't toxic, but isn't reliable enough and too expensive, and so toxic preservatives are added (almost all preservatives have toxicity, since they are designed to kill bacteria, its just a matter to what degree they are toxic.)
Many immunizations are made by injecting a contagious disease into a living, developing egg. This makes all immunizations made this way a possible trigger for the person immunized to become allergic to the proteins in eggs or egg whites. This is an inexpensive, healthy, staple food for many people, and its really unfortunate if you have to eliminate eggs from people's diets. By stimulating the immune system at the same time as injecting eggs into a person, the similar proteins in eggs to living human tissue can cause auto-immunity to develop.
Mode of Delivery
Getting exposed to a disease by having it injected is not the normal way a human gets exposed to certain diseases. And so our immune system can become confused by encountering a disease which is already in the bloodstream when it usually presents itself at the usual 8 "entrances" to the human body (the eyes, nose, mouth, vagina, ect.) These entrances are all covered with a specially-designed protective surface called mucous membrane. This surface has special ways to react to contagion that the bloodstream doesn't have. It produces phlem, (mucous,) and other excretions to stick to, contain or wash away the bulk of the disease organisms, and has easy access to the bloodstream where immune cells can grab the invaders without being overwhelmed. This normal immune reaction is bypassed with an injection, causing the immunity to this disease to be unnatural. It tells the body to look inward for disease, instead of outward. It causes the immune military to be harassing the natives instead of the invaders.
It is this reason that many newer immunizations are now being developed to be given by spraying into the nose, to better mimic the typical exposure to contagions.
Age of Delivery
The human immune system is not fully developed and functioning the way an adult's is for many years. This is the advantage of breast feeding and the reason people take colostrum (bovine immune cells made right after birth of a calf.) The infant inherits some of the mother's immunity to diseases she has been exposed to through the initial breast milk. He can sometimes inherit a faulty immunity to certain allergenic foods this way, too.
So if you are trying to get the same immune reaction an adult gets to happen in an infant, it just isn't going to happen. So you have to re-immunise several times as the child develops. This can be a waste of resources if the child wouldn't normally need full immunity for many years (such as immunizing against diseases that primarily affect adults, like sexually transmitted diseases.)
Infants and the elderly react differently to almost all medications because of how their livers clear the blood and for other reasons. They are a more vulnerable population and should be given special consideration with medications, dosages, and other issues.
For instance, there is the Tylenol issue -- you used to have to give a different dose to babies than adults, not just because of the size, but because it was less diluted so that the baby would have to swallow less of the drug. This lead to confusion about doses and many children got overdosed causing liver damage. There is Rye's Syndrome, which is caused by giving a child aspirin during an illness. Drugs that act as stimulants to adults, when given to children have the opposite effect -- to calm them down. Because of aging, the elderly metabolize drugs differently and at different rates than other adults, their livers just aren't as effective at removing them, and so they stay in circulation in the bloodstream longer, sometimes leading to a build-up of the drug in the body and thus to overdoses. And there are a lot of other differences in very young children, and the elderly.
The main issue here is that you can't experiment on children, so all the vaccinations are researched on adults. Every time a child takes a medication right after it is released to the market, takes a risk, because they are the true Guniea Pigs.
And because female adults often can be pregnant and not know it, most research is done on adult men. So almost all the knowledge we have is based on adult men's bodies. This completely ignores the changes in hormones and other functions between adults and children, and fertile and menopausal women.
Of course, all this is balanced by the true concern that we need some kind of defense against a true epidemic of a deadly disease, like Polio. However, once a disease is very unlikely, such as when the disease is gone from all but a few remote locations in other countries, the vaccination is not removed from the schedule. They keep them up and the list of vaccinations keeps getting longer. No normal person would come into contact with every deadly disease known to man. So why put so many people at risk of side-effects and complications, and mistakes, if the disease is unlikely?
I think that in the past we could look to eradicate diseases. But now we know they mutate, and evolve, just like we do. So we can't completely rely on vaccinations to solve all of our contagion issues. Besides the fact that almost all deadly diseases still exist in labs around the world waiting to use in case someone "needs" them for weaponization. We have to have a multiple-level strategy for dealing with disease, and if we only rely on immunization, we will not fund research to find other ways to deal with health, wellness and disease.
Disclaimer: I am not a Doctor or Researcher.