Open source beats proprietary software, that's what's happening now. Ubuntu thinks to make a favour to their users by blacklisting the FLOSS b43 driver and installing Broadcomm's wl, perhaps believing that things might work more smoothly. Well, that's not true: for example WPA2 doesn't work.
This is what I did to make it work.
I basically deleted (or moved somewhere else) the blacklist file /etc/modprobe.d/blacklist-bcm43.conf.
Then I uninstalled the Broadcomm dritver:
apt-get purge bcmwl-kernel-source
I also commented out the relevant line in /etc/udev/rules.d/70-persistent-net.rules.
Okay, maybe you still need the proprietary firmware, b43-fwcutter or something like that, but it's at least good news that now everything works fine (after just a reboot) and I can use any modern Wi-Fi network.
I'm not sure all of the above is necessary. Certainly b43 works better than wl, as far as I can tell. Certainly Ubuntu does a great effort in tweaking GNU/Linux to give their users a better experience, but sometimes it's more of a problem than a solution. Perhaps it's just time to relax: the regular Linux drivers (the ones that the kernel or udev would automatically load by default), well, they... just work.
Note: in case you wonder:
# lspci -n
02:00.0 0280: 14e4:4727 (rev 01)