Hi (old question I know, but I'm still having this issue and this is top of the search list for this problem)
I've done some testing and:
The problem seems to be related to the extras.
When you initially double click on a movie with extras, it will try to open the menu (like its a DVD); sometimes, apparently at random, this doesn't work (I suspect it might be to do with changes made to the info, like title, artist, or 'album' - but I've changed them with several movies and they still play fine so...Apple, get on it...come on, you can afford to set it as some intern's pet project over the summer right?)
Point is, I've found two ways to get the film to play:
1. find your film's file in Finder(/explorer on PC if this is happening on PCs too), tell it to open in iTunes, the film will play.
You can then safely close it completely and come back to the same point (as long as you haven't unchecked the 'remember playback position' option) because now opening it in iTunes normally is set to skip over the extra menu portion (this will reset when you get all the way through the movie). This doesn't add a duplicate file or entry btw.
2. Change the media kind (Film Info, Options, first dropdown menu) from Film to Music Video (or whatever) and OK the change. The film itself will now play like any other video (though you'll have to remember it'll appear in a different tab in the library). Again, once it's started playing, you can get a second (or however much) into it, change it back to a Film and it will playback from that point. Can't vouch for whether this will reset to opening to a blank screen after the film has played through, but I suspect so.
Neither of these will get you access to the extras themselves back...so...seriously; Apple, get on it!...
Hope that helps someone.
If so, give the next homeless guy you see enough cash for a sandwich for me.