Update:iLounge now reports that this may not work as the 24-hour rental trigger is automatically invoked when streaming to the Apple TV.
Even though the new Apple TV is a streaming-only device, you can still rent and watch TV shows and movies right from within iTunes. But, as MacRumors points out, Apple may not have thought this whole streaming-only plan out thoroughly because you can now rent shows and movies without abiding by the 24-hour rental policy that is standard in iTunes rentals.
Rentals used to work by actually moving the video files around to the different devices you wanted to watch them on within a 30-day period. Once you start watching these videos, however, the 24-hour countdown begins before you'll no longer be able to watch the rented content. Because the Apple TV doesn't have storage for moving videos over to, these rentals play directly from your iTunes library on your Home Sharing network.
This is where the bug comes in. By doing the following 3 steps, you can have 30-day rentals instead of 24-hour rentals:
1. Rent and download a TV show or movie from iTunes on your computer, but don't open or play it as this will start the 24-hour counter
2. Start playing the video on your Apple TV. You'll notice you get no warnings about the 24-hour rental.
3. When you check on iTunes, you will notice that you still have "29+ days remaining" on the video file.
MacRumors does note that because the Apple TV hasn't been out for 30-days, it's hard to test whether or not this bug will work long term, but you may still be able to watch your rentals multiple times over multiple days, just as long as you don't trip the 24-hour counter in iTunes. Plus, there's no doubt that Apple will soon issue an updates that resolves this issue in either iTunes or the Apple TV. So don't expect it to work forever.