I have a Broadcom Wireless Network Adapter and I had all sort of problem with the standard driver, Broadcom STA Wireless driver or wl that the module is called.
To identify which Broadcom chipset you have. Run:
To identify which modules (driver) you are using (running):
I had the STA or wl module running. To remove all possible Broadcom modules.
And to really remove the default STA or wl module, also remove the debian package. After the purge, that remove configuration files as well, I double run apt-get with remove autoremove, which will remove unused package and finally I run clean, to clean the apt-get cache. All for precaution.
Now you must test which driver/module that suites you best. I started with the b43 driver/module.
To load the new module/driver.
Now test you installation, if successful reboot and double check, that everything is working correctly..
Other possible driver are b43legacy package firmware-b43legacy-installer and LP-PHY package firmware-b43-lpphy-installer.
For more hardware commands, please read http://magnus-k-karlsson.blogspot.se/2013/01/how-to-install-atheros-ar8161-ethernet.html