Can't get BCM4331 wireless working right

I had the same problem. It was so annoying.

Finally, I resolved my issue by installing Ubuntu 13.04 (daily build, 20. March). Now, I am writing this answer on Ubuntu 13.04. The wireless issue is solved completely. Other hardware is working perfectly fine.

By the way, the wireless driver is installed by default and works out of the box. The driver is "wl" and not b43.