This has to be a common problem.
Put some static text in, and alias it.
Stretch your movie so it plays for a few frames.
When you play the movie, the text is crisp (aliased) in the first frame, but blurry in all the others. What’s up?
Note: sometimes putting the text on whole pixel x and y positions fixes the problem, but sometimes it doesn’t - and I shouldn’t have to put stuff on whole pixel values anyway.