I think I have fixed the problem. I unplugged the AppleTV and plugged back in (since I could find no way to reboot via the UI, #fail) and now my programs seem to be playing with no problems.
Another odd thing though was that I had to "reboot" a couple of times as it failed to fully load the menus the first two times and the remote was completely unresponsive... It starting to sound like I may have a faulty unit...