Once the rental is downloaded, you can watch it on your computer or transfer the rental to a supported iPod, iPhone, iPad, or Apple TV (1st generation):
- Connect the device and select it in iTunes.
- Click the Movies button.
- Select the movie, and then click Move.
- After all movies have been moved, click Apply in the lower-right corner of iTunes.
You must be connected to the Internet to transfer a rented movie.
I copied the text from here http://support.apple.com/kb/HT1390
This is old, but I believe that it still applies as well.
FIXED FINALLY. I was having the same problem. It was not transfering the movie because my parental restrictions were set too low on the iPad. No error message, just wouldn't transfer movie. All you need to do is go to Settings->General->Restrictions and make sure that they are set correctly.
Come on Apple, give us a simple error message to let us know what was wrong...