If you have learnt a piece with one teacher and got it to a reasonably polished state, and then decide to play it for another teacher in the hope of further improving it, is it common for the second teacher to pick up on things that have not by noticed by the first teacher? It sounds like a rather silly question, as that's the whole point of going to the second teacher, but would this reflect badly on the first teacher?
You don't need to learn on a Steinway to be a good pianist?