Myth Busters films a lot of footage with $249.00 GoPros. If you look in the background of a lot of their 'talking head' shots you'll see GoPros all over the place. That footage winds up on TV and you won't see any wiggle.
I have 16 hours of in car from our last LeMons race which has no wiggle, not even when one of our drivers was clipped from behind and spun at about 65-70 MPH, sending him off into the weeds. And that's with a ~$400 camera. One of my personal vids:
The original is much higher resolution, YouTube downgrades them over time. BTW, that camera setup was a ~$1k MotoCam rig which I bought in, IIRC, 2006. All my current YouTubes were shot with that MotoCam. I've retired it in favor of a cheaper Race Optics setup with better resolution but I haven't edited any vids from the new setup yet.
Lots of the YouTube LeMons videos are shot with those ~$100 Kodak etc digital cameras, a few have even been done with iPhones or similar.
I see real nice steady footage with those cheapie 'Flip' cameras too. Here's an example:
This guy paid, IIRC, $129 for a Flip and made his own mount. You can see the camera's reflection in the mirror. (Side note: the stuff he posts looks like so much fun that it makes me want to sell all my crap and use the $ to build a Midget or MGB vintage racer.)
Cameras are so light now that making a rigid mount is simple. If a camera is helmet mounted, the helmet weighs much more meaning that it and the camera will move together, making it look like a megabux steadi cam rig.
Now, my old VHS-C camcorder shook like a dog shitting peach pits even with a $175.00 i/o port vibration isolation mount.