Well, now that I have new install, I am not going to be touching THAT button any time soon...
I did run /usr/lib/linuxmint/mintWifi/mintWifi.py once when I had the system messed up. Off my memory, Broadcom 4306 was found as PCI device, but the system found no wireless device (no wlan0, only lo and eth0). I assume this is the same result I get with iwconfig.
I am guessing that Synaptic updated hal from Hardy's repo. I have access to another laptop that uses Broadcom 43xx that runs Hardy (my wife's), and that one is completely up to date, and its wireless is working fine using fwcutter, so whatever that happened to hal is conflicting with Mint, so it seems.
Broadcom wireless has always been touchy anyways, but it does make me wonder if any other hardware is affected.