So it turns out the new Broadcom b43 drivers, since kernel 2.6.24, have a really nifty feature that allows you to create a new virtual interface to monitor data. And it supports injection out of the box!
To use it (I'm using Ubuntu), just type these commands:
sudo iw dev wmaster0 interface add mon0 type monitor
sudo ifconfig mon0 up
Now you can use airodump or your favorite monitor mode applications on mon0:
sudo airodump-ng mon0