Wow what a stupid bug to have. Does this happen with every Catalyst drivers package of only with certain ones? Also have you tried disabling GPU acceleration in flash? I heard that can cause the video card drivers to lock up. Also update flash to the latest version.
It seems to be every driver version, and GPU acceleration in Flash makes no difference (tried both ways). But it's not Flash-related--it's a problem with any video overlay. There's the same problem playing video in any other applications (Windows Media Player, Media Player Classic, etc.).
See
this thread on the Bitcoin Forum where it has been discussed extensively, along with
the official "GPU lockup if running OpenCL and playing video at the same time" thread on the AMD OpenCL forum. It was a problem a year ago with different cards and different drivers, and then resurfaced again now with the 6900 series.