Hello tmilowski. Actually, Apple allows a bit of a grace period on that 24 hours (shhh! don't tell the movie studios!). How much of a fudge factor, I don't fully know, because you won't find anything advertised about it.
First off, I'm sure you are aware that you have 30 days to watch a downloaded movie that hasn't been started. Secondly, the general rule is that you have 24 hours to finish viewing a movie you started, BUT I have found out you can exceed that 24 hours.
For example, let's say I watched half a movie and AppleTV tells me it is ready to expire in 2 minutes. If I start that movie up again before it expires, AppleTV/iTunes lets me watch the rest of the movie well past the expiration time.
I'm not sure how far you can bend that grace period, but I have viewed several rentals beyond their expiration times.