Health claims:
Passive mm-wave scanners do not produce radiation. The active mm-wave scanners use non-ionizing radiation which has been studied and shown not to cause cancer. One study even suggested it might reduce metastasis:
http://onlinelibrary.wiley.com/doi/10.1002/bem.20208/abstrac...
You'll pick up far more radiation on the flight itself at a fairly low 5 mrem (50 µSv). Even that would only be a significant factor if you're part of the flight crew.
http://hps.org/publicinformation/ate/faqs/commercialflights....
It's true that the machine itself hasn't been studied much, but the type of radiation it emits has been studied extensively. Barring any novel delivery system, that's enough. By analogy, you don't need to study the health effects of every single x-ray machine because we know what x-rays do. You just need to know the machine's dosage and wavelength. The lack of health concern is more than a stab in the dark.
Invasion of privacy:
Yes, the scans are absolutely an invasion of privacy. So is submitting to a pat-down. The problem isn't the scanner - it's the bureaucratic nonsense that makes the security state and the TSA possible.
I believe a business should have the right to search you before coming on board if they want to and you agree, but they shouldn't HAVE TO. Flyers should have an option between airlines that use the security measures the market determines people actually want.
Specifically, the "naked body" invasion:
It does us harm to spout misinformation in our quest for privacy and freedom. The machines no longer store or display images of your body - they store and display images of a generic body with the data received from you.
http://www.wired.com/threatlevel/2013/01/tsa-abandons-nude-s... (the initial announcement)
http://www.nydailynews.com/news/national/tsa-completely-remo...
I dislike the TSA and government paternalism more than almost anyone, but we're getting caught up spreading misinformation and nonsense when we should be thinking about how to get our personal freedom back.