#1 - Still need to verify the altitude (provided the transponder is capable of it)... "radar contact, squawk normal, say altitude".

This is one of my pet peeves. It is the responsibility of the controller to be sure that his display is accurately representing the actual altitude of the aircraft, but it is the pilots responsibility to report his altitude on his initial call. There should be no reason the controller needs to ask if the pilot checks in correctly.

The instructor may also want to consider visually checking the checklist as the student performs it to prevent this from happening again, or something similar. After all, the instructor is the PIC...