Don't put a camera, or anything else, on your helmet. It's not safe if you crash. Put the camera on your handlebars.

Although a 2GB memory card lets my Oregon Scientific ATC 2K record my entire ride, I find it's too battery hungry to record my entire commute every day.

There's a fair bit of criticism of cops in this thread, so let me add a counterpoint: where I live, the cops are great about bikes, and in 5 years of riding I've had only positive interactions with them. Taxis and bus drivers are another story.