Mr. Monk and the T.V. Star - S2-E12
Plot hole: Unless I missed something, the killer didn't wipe his prints off the knife he used to kill his ex-wife.
Mr. Monk Goes Back to School - S2-E1
Continuity mistake: Mr Monk completes his name on the chalk board at the beginning of class, but when class is dismissed the 'k' in Monk is incomplete.
Suggested correction: After he wrote his name, he says "what's up with that k?" and erases it. He started to re-write the k when he got hit by the eraser, leaving it unfinished.