Not all videos will play on the iPod, despite playing in iTunes. Highlight the video in iTunes, then click on *Advanced/Convert selection for iPod/iPhone* . Then, take the suspect version off and use the converted one.
Conversion can take a while, so don't plan to use iTunes for anything else until it has finished. Also, even though it has been converted by iTunes, it still may not play. One of my videos, converted by iTunes, would not play and actually locked up the iPod until the battery had drained. Needless to say, I've removed the video from my iPod.