If the videos are being embedded as native Rich Media Annotations (the default in ID CS5.5) then playback is handled by Flash Player - this can only read certain types of video and audio track. Some MOV files are supported, some are not.
Best option is to convert the problematic MOV files into H.264/AAC (MP4 or F4V files), using another app - if you have Adobe Media Encoder it can do the transcoding very easily.
If you open the MOV file in Quicktime you can inspect the codec info and see what it's used.
Thanks for the reply – All 3 MOVs are in H.264, and I've just tried converting it to an mp4 in quicktime, which works in the pdf, but no matter what setting I use to convert the mov to mp4 the quality is rubbish! I just don't understand why it would recognise 2 different mov files but not the 3rd one, which was made at the same time, using the same method and with the same settings....
Just for the history and for the google purposes.
I've faced the problem by myself and after some investigations found that the reason is in wrong characters in the file name. In my case it was the & sign in the name. Removed it - and the same video worked like charm. No gray rectangle, just my movie working.
It is indeed the strange thing, since you can add the video with & in the file name in acrobat just fine.