Everyone from dental hygienists to radiologists must undergo health physics training before being allowed to use an X-ray machine on human subjects.

Everyone, that is, but law enforcement.

Thanks, FDA. Good job.

Because the law enforcement devices emit such a tiny rate of dose that it is impossible to harm someone while using it.

"A person would have to be screened more than a thousand times in one year in order to exceed the annual radiation dose limit"

If you'd said, say, 50000 times, I might be more swayed, but a thousand seems easy to hit if these are widely used. If they're used daily, just passing two on a commute is enough to go over the limit.

Oh, well, that's different, then. As long as the cops and TSA goons are qualified to tell when the machine is malfunctioning, miscalibrated, or otherwise going full-Therac 25 on us, we're good.

Those machines should be built to be at least as annoying as new cars - i.e. if anything breaks, any diagnostic fails, the machine should not start. They probably aren't built that way though because - unlike with cars - there isn't a profit motive to do it this way there.

Or once with the wrong settings or too long of an exposure. Or the operators get the scattering effects wrong...

Easily achievable with indiscriminate screening. How many times a year do you pass under the speed meter?

Self reporting. Excuse my scepticism, it doesn't have a great track record. Additionally, the users are not exactly experts on radiation safety or knowledgable about radiation dosage, and I don't see how manufacturer reporting can cover what happens in the field.