There are a number of problems with a vaccine solution to the Covid-19 pandemic, even assuming that the vaccine is safe.
Vaccine effectiveness is generally age-dependent. They are more effective in younger people than in older people, who are the most vulnerable to Covid-19 infection. The 90% effectiveness of the Pfizer vaccine is for the study group as a whole, and the age distribution of the volunteers is likely to be younger than the general populations in countries that have been badly affected (all of the 'data' that were released were contained initially only in a press release, and not in a published study, I don't know if that situation has changed in the interim).
Using the flu vaccine as an example, a 75% rate of inoculation in vulnerable aged people is considered a very good rate of vaccination. The flu vaccination is typically about 75% effective, meaning that in such a scenario the flu vaccine gives around 56% coverage for this age group. The 44% not covered comprise those who were not, or could not, be inoculated, and those who were inoculated but in whom the vaccine is not effective.
Pfizer claims only that their vaccine causes a 90% reduction in symptomatic cases and not a 90% reduction in infections due to the virus. It may be much less effective in preventing asymptomatic infection. In turn, a vaccinated, asymptomatic individual may still be able to spread the virus to others without realizing. This is currently unknown.
We do not know yet how safe the vaccine is in older, vulnerable people.
Given that there is likely to be a significant proportion of older and otherwise vulnerable people who will not have direct vaccine coverage, they will need to rely upon any kind of herd immunity effect in the population, assuming that the complication mentioned above, of not necessarily preventing infection and transmission, is not a factor. The herd immunity threshold might be as high as 60-80%. If it is 60%, then about 67% of the population will have to be vaccinated, meaning that the number of doses required is about 134% of population, as it is a two-dose vaccine. It is difficult to persuade younger people to get vaccinated, so getting two-thirds of them vaccinated will be no easy task, given that it is likely to be legally (and certainly ethically) impossible to make vaccination compulsory for adults. This is a completely new vaccine technology, so people might be understandably wary of voluntarily accepting such an inoculation, as there has been no long-term monitoring of its safety as it is brand new.
There are of course problems with delivery of this vaccine, as it needs to be stored at cryogenic temperatures, much below those in typical medical refrigerators in doctor's surgeries. A vaccine centre will therefore need some kind of cryogenic refrigeration plant.
