"This movie requires QuickTime, which is not supported by this version of iTunes" - https://discussions.apple.com/thread/3832288 - switch iTunes to 32 bit mode.
iTunes 10.4 for Mac: Older media files may require iTunes to reopen in 32-bit mode - http://support.apple.com/kb/TS3771 - "iTunes 10.4 or later on OS X Lion opens by default in 64-bit mode. However, some older media files in your iTunes library may still rely on QuickTime to play, and QuickTime only runs in 32-bit mode. In order to play media that encounters this issue, you will need to open iTunes in 32-bit mode first."
I find this deplorable that you purchase videos from ITunes and can't play them. You have to force your application to work with a 32 bit process.
I tried this, ITunes said I had to reauthorize my computer. Understand the technical reasons, as I'm in IT myself. However, this needs to be resolved. I've got several videos/movies/TV etc that have this issue, and have to open them in Finder, then right click and watch them in the QuickTime app. These videos are not old, they are part of an ongoing season, downloaded via Season Pass.
When you move the files to another location and reimport or delete them and redownload, the issue is resolved.
Fix the issue Apple.
Being a big advocate of rtfm-ing you will undoubtedly have noticed:
6. Apple involvement. Apple does not formally provide technical support on the Site.
The people reading and responding in this forum are just other Apple product users like you, not Apple itself. Apple uses its feedback pages (not this support forum) for garnering product feedback or suggestions. Apple Support Communities is an end-user to end-user (i.e., users like you helping other users) technical issue support feature. You should send feedback via:
http://www.apple.com/feedback/ - Apple products feedback links