I was with a student in one of our club Arrows. We put the gear down
and got green lights for the 2 mains, but not for the nose.

The nose green light was flashing, as was the yellow "gear in transit"
light. Both were flashing about twice per second, and in opposition
(i.e. as the green went on, the yellow went off, and vice versa).

The maintenance people were unable to reproduce the problem and the
plane was returned to service. Best guess is a slight misalignment of
one of the limit switches.

What would you have done? Would you have cycled the gear hoping to fix
the problem, or would you have accepted the possible unlocked nosegear
in exchange for the known locked mains?

My experience with an Arrow is that it's usually a misallignment of the
microswitches which causes the 'gear not-locked' indication(s).

Something else to try is to use the emergency 'drop-gear' lever and
also some porpoising to nudge the wheel into the locked-position.