Movie rental playback
I rented a movie on apple tv, it has technical issues, can't play movie try later, all other channels work fine
iPad 2, iOS 7.1.2
This will be due to the network. Other content adjusts to the connection, whereas iTunes is fixed rate and will attempt to load a portion before playback begins
What is your current connection via speedtest.net
Make sure DNS is set to auto (settings - general - network)
If on wifi try Ethernet