I am having this same problem too. I have seen several responses to other people who have posted looking for help with this same problem. So, far none of his responses have seemed to be effective.I think Apple has really dropped the ball with this update to 6.2.x. I can do everything I have always done with Keynote but play videos. Yes, they are all encoded using the H.264 codec. Many were even created using iMovie. And, they all play when you click on them, in edit mode, but when you attempt to run a presentation every video plays for less than a second and then quits. This problem has occurred ever since they started giving iWork away, post the official release of OS X Mavericks.
The current project I am working on I am using video clips I created with iMovie and they still will not play in presentation mode. I am afraid we are not going to have a solution until Apple owns up to the error it has made and addresses it with new code.