Does using a movie poster in a book of movie reviews and critiques count as fair use?

Fair-use questions are always extremely fact-dependent and difficult to answer. As you know, there are a number of statutory factors, no one of which is by itself dispositive. The facts that you are using the poster for criticism and that your use does not deprive the copyright owner of the economic opportunity to sell copies of the poster should be extremely important to this determination. However, you are using the whole of the poster -- not merely some extract from it -- which is a factor that weighs against you. In these circumstances, your publisher may insist that you obtain permissions. Such permissions are liberally granted and not difficult to obtain. It is impossible to state definitively, from the facts that you have posited, that this use would be deemed "fair."