The discussion of salaries (both of teachers and police) is missing something crucial: locality and cost of living. Teachers near @jca make $100,000 because she lives in an extremely wealthy area of the country (in fact, telling us that fact about local teacher salary reveals that she lives in one of a very small number of locations in the US, though I won’t name them out of respect for @jca‘s privacy). Police in her area follow a similar (though lower) distribution curve. Police and teachers in @ARE_you_kidding_me‘s area also paid similarly, though in that case it is the teachers who are on a slightly lower distribution curve.
If you look at the whole picture, teachers and police officers tend to make roughly similar amounts by region (with variations largely depending on local politics). And both tend to make relatively low-to-moderate salaries that are disproportionate to what they are expected to deal with. Therefore, we see similar problems with both: a small number of dedicated people who do their best and stay out of the news, a large number of mediocre workers who are just trying to get by and vacillate between doing a decent job and abusing their power, and a small number of people who seem dedicated to ruining it for everyone.
We also see the same sort of code of silence, with the large group of mediocre people protecting the terrible people in order to keep their own asses covered (since they also abuse the system—just not as often or as flagrantly), and the small number of dedicated people frequently being intimidated into staying silent (and often being driven out of the institution when they finally do speak up). You get what you pay for, and these are two professions where Americans have more or less decided to roll the dice. Both professions are in need of various reforms, but better pay and increased selectiveness is key to each.