What might happen if I receive flight instruction in a plane with an airworthiness deficiency? Let's say I were to a day VFR flight with a new instructor, in hopes of eventually pursuing Sport Pilot - Airplane privileges (U.S.A.)

During the flight, I notice the plane has a minor airworthiness problem. It doesn't affect the safety of the flight, but something required is missing. The magnetic compass, for example, is loose in the glove box instead of mounted on the instrument panel. I bring it to the instructor's attention, he downplays its significance and says he plans to get it fixed in a few weeks.

The flight goes otherwise well. The instructor fills out &amp; signs my logbook in the usual way.

Is this legal instruction time? If this instructor were to get in trouble over instructing in an un-airworthy plane, could that void those instruction hours' applicability towards the sport pilot hour requirement?

(and the more subjective question: practically, how worried should I be over something like a missing compasss? Is it really as minor as I think? Anything I should be looking more closely for before I fly again with him?)
It can’t void the time, but if an Inspector ever caught a CFI doing something like that, he’s in big trouble.  And more importantly, that CFI should know better than to do something like that in front of a student.