Box shape of the gopro is not ideal for use on a helmet.
In general I'd recommend the lipstick form factor for helmets.
There are new models of the lipstick models being released regularly, one was launched a few weeks back for firemen's helmets $290. (but it is lower res 720p than gopro 1080p, gopro also does 5mp stills)
Wix.com - Website built by firecam based on Blank Website
Gopro is highest quality with excellent auto everything, they are being used regularly for short shots in TV commercials. Beware that transcoding is required to edit the footage in some apps. A clip-on monitor screen will be launched soon for the gopro. I hope they make a version in lipstick form factor as they are ahead of the rest of the field.
Beware that being a rolling shutter cmos sensor they impart a "jello effect" on the image if the camera is oscillated or vibrated. Not critical for home use but a deal breaker for high end data gathering.
Rigid plastic self adhesive velcro pads are a reliable, cheap form of non permanent frangible mounting that does not compromise the integrity of a helmet.
Mickjoebill