In order to gain a good reputation you need to be good in the judgment of a VAST majority of people that are informed by their own experience or by a trusted source. On the other hand: In order to get a status of bad reputation you don't need a majority of consensus, a few people's opinion are enough (people who are really well informed and that formulate their judgement in their own minds). I think this is fair.

I agree with the other people who have answered. I'm a native speaker, and "this teacher has a good/bad reputation," sound perfectly normal to me!

Basically, having a good or bad reputation can refer to people and places. To answer your question, for example, whenever one has a bad reputation, that means that most of the people judge him negatively or make a nasty opinion. After all, this is my point of view.

Yes, schools, teachers, and shops can all have good or bad reputations.