I have been experiencing the same error a lot of Apple TV users have when watching Netflix. Everything will be fine, you can navigate the menus,and see your instant queue. But when you try to actually play the video, you get an error message (111 or 112).
The easiest way to get past this is to power down the Apple TV completely. Putting it to sleep doesn’t always work. Unplug the device and then plug it back in. Works every time (so far).
I’d love to see this issue, whether it’s with Netflix or Apple, fixed soon.