These are very complex issues so I will do my best to unpack them to the best of my ability.
The facts presented are by and large factual but a least one of his assumptions is dubious. Overall it was a very interesting video.
To address the points he raises we must first understand herd immunity. Herd immunity is the general resistance to a pathogen that exists in a population because members of that population have been exposed to a disease in the past. It manafests in two ways.
A) In the natural immunity of individuals who can no longer contract the disease because they have already been infected in the past and fought the disease off.
B) In a secondary form passed from mother to child via antibodies in breast milk. A mother with natural immunity can transfer antibodies and temporary protection to a newborn.
It is important to note that this second group infants are not truly immune to the disease. Their protection lasts only as long as they are breastfeed and once they are weaned they have no residual immunity and are 100% vulnerable to the disease. Immunity transferred by the mother is a temporary protection only who's purpose is to protect a newborn until it reaches any age when it's immune system is more developed and better equipped to survive.
Now with that said Dr. Wakefield makes several arguments regarding herd immunity.
1. That our vaccines do not result in as strong of an immunity as natural infection so the transferred protection via breast milk to newborns is weaker. Thus newborns are more at risk if they are exposed to the target disease then they would be if their mother had natural immunity.
This is true. However, it must be noted that under the natural immunity scenario the infant also loses all immunity when he is weaned around age 1. The potential window of heightened vulnerability exists but it lasts only from birth until or the date of weaning or vaccination whichever comes first. After weaning the unvaccinated child has no protection from the disease the vaccinated child does.
2. That mortality rates from measles was falling already before vaccination so maybe that process alone (better supportive care, health, and nutrition would continue to reduce the fatality rate to zero.
This was the only point he made that is highly speculative and extremely unlikely to be true. Measles is not going to just turn into the common cold because we have good nutrition and are healthy. Unless there is some scientific breakthrough that cures the virus it will always be a very serious potentially fatal illness.
3. That our vaccine policy create a dependency on vaccinations. That there is a possibility that these diseases could mutate around our vaccines or vaccines could suddenly be withdrawn and if that occurs the population could be worse off then if it had maintained its natural immunity to the disease.
This was by far the most interesting of his arguments. Here he presents a powerful argument. This argument can be best understood by looking at antibiotics.
Say you had an individual sick with a deadly bacteria. It would be highly unwise have that individual take just enough antibiotics to keep the disease from killing him but not enough to cure the infection. He becomes dependent on the antibiotic and eventually the bacteria might mutate and your drug won't work anymore. Dr. Wakefield is essentially saying we are doing this with our vaccination policy when we releasing vaccines like the mumps vaccine that are not capable of actually exterminating the disease.
I am sympathetic to this last point. However, it is not an argument against vaccination but against foolish and unwise vaccination.
A vaccination campaign should be a declaration of war against a pathogen an all out attempt to kill a disease worldwide like smallpox was killed. That kind of campaign is akin to giving a big dose of antibiotic (a poison) who's use kills the disease and thus cures the patient. This type of campaign is wholly justified scientifically and morally and we have seen it done in the case of smallpox.
Once you transition from that to a management strategy where you only suppress the disease but allow it to fester and smolder on in the periphery or when you introduce vaccines that are incapable of actually exterminating the disease then you indeed must question what the long term ends of your effort is.
However, all of this does not mean we should not vaccinate, any more then the risks of antibiotic resistance means we should stop using antibiotics. However, it may mean that our current approach is... lacking.