This problem seems to have started around October 28, it appears to affect content purchased only on other devices but played on the Apple TV 1.
There have been other workarounds suggested from time to time, but I have found the simplest solution is to purchase something on the Apple TV 1 directly (There may be free content in some locations and this appears to work just as well).
Once the content has been purchased, it will not only play as normal, but will also allow all other content purchased on other devices after October 28 to play as well.
Some have reported that it's necessary to restart the Apple TV before and/or after purchase, but I found it worked without.
I did have the 'not authorized' issue before that was resolved by purchasing content directly on the ATV. I did try that work around this time but it didnt help. When I had that problem before things would sync, but not play... this time they wont even sync and I get the "format not supported" error.
I had this problem too.
Found the answer - it is something to do with iTunes opening in 64 bit mode under Lion. No idea why it does it, but I found it also stops you playing those files in iTunes itself as well as the syncing problem to the ATV1.
Follow the instructions here to have it open in 32 bit mode and you'll find they now sync to the ATV1.
Hope that helps.