MBP-10.10.4, AppleTV Gen 3, Ipad Air 2 - IOS 8.4.
Imovie Theatre works on the MBP and the iPad, but not accessible from the Apple TV. Error message: "Cannot Connect to iMovie Theatre. There may be a problem with iCloud or you internet connection, Try again later." iCloud Photos are viewable, and other apps work just fine.
My Apple TV is doing the same thing, for the second time! After trying several things, such as logout of iCloud, reboot the Apple TV, etc., iMovie Theatre was still not accessible. I fixed the problem the first time, by doing a reset to factory conditions on the Apple TV. After logging back into iCloud, the iMovie Theatre was available, and I could view the movies. The agravating thing about a factory reset is, you have to login to all of the apps that you use again, that's not a quick solution. Now, it has quit working again. I don't use the Theatre frequently on the Apple TV, just when I want to show someone some new movies, so I don't know when it stopped working the 2nd time. I have uploaded some more movies from my MacBook Pro, maybe that breaks it.