"Do some shows just have indefinite "previews" until they decide they have it right?"
It's pre-determined. The show sets an opening date and they have until then to tinker. Occasionally the opening can be delayed by a few days if more changes are needed. But it sends out a very bad signal.
"And what about the people who are PAYING to see a preview? Please don't tell me that they're allowed to stop mid-play to change something, or address one of the actors."
Oh god no! The creative staff makes changes between shows. The only time I'm familiar with a show being stopped during a performance was b/c of a mechanical set malfunction. Many preview tix are less expensive that once the show has opened b/c it's still in a state of flux.
"What is the difference between a preview and a DRESS REHERSAL?"
Think of a preview as a Dress Rehersal with an audience.
....but the world goes 'round