I have the same exact issue. Well, half of it anyway, the strange desktop corruption. And on a 7850.
It doesn't appear in screenshots, and I can reproduce it easily by scrolling in Chrome. For example, I scroll one line, the corruption appears, I scroll another line, they disappear, and I can repeat that pattern dozens of times.
My assumption was that they had screwed up browser hardware acceleration or something, but I wasn't certain if chrome was the only cause.
I don't have any problems in games at all, whether BF3 or Skyrim. I ran Furmark for awhile too, but everything seems fine.
My guess was either the hardware acceleration, the idle clock profile being changed so low that 2d stuff was having problems, or some other issue with clock profiles switching. Or some combination thereof.
I haven't really had time to delve into it, but you're not the only one. I haven't bothered to revert, but I assumed that would solve it. This issue immediately appeared only after I went from 12.7? to 13.1
Edit: I also didn't bother to actually turn off hardware acceleration in Chrome or experiment with different browsers. Like I said, I haven't had the time. Maybe this weekend I'll see what I can discover.