I think those wear dimples on some new tires are cute, but I don't worry about them.
Too many flats, which I define as a couple flats in a couple weeks (usually after going 6 months or more with no or very few flats) is my warning that the tougher outer rubber is worn down. If I miss that "indicator" I give thanks for clean roads and wait until I see threads. (Although I once rode an out of town metric with threads visible that I didn't see until the night before, far from home!)
Flat spot on the rear tire may indicate the tire's wearing down, or maybe you just need to pedal hard on a few turns to round the tire back out.