Mr. Monk and the Girl Who Cried Wolf - S3-E6
Corrected entry: The teacher does not see the pretend murder victim behind the window, even though she should, as by now we all know that Sharona is not crazy. (00:28:50)
Mr. Monk and the Blackout - S3-E3
Corrected entry: Monk insists on taking the stairs because he has a fear of elevators, but in previous episodes he has used elevators quite contentedly.
Correction: In this episode it isn't that he is afraid of elevators, but he notices that the floor of the elevator car doesn't line up properly with the floor of the room, and is thus "crooked" and "unsafe." This is why he insists on taking the stairs.
Mr. Monk Takes Manhattan - S3-E1
Corrected entry: The captain refers to the DA as a "guy" just after the New York policeman calls her "she", indicating she is female. (00:09:45)
Correction: He may have meant the man that the DA was going to help them meet with, rather than the DA herself. What the captain said was ambiguous.
It wasn't really ambiguous. But you're right, the Captain was referring to Warrick Tennyson. That was the whole purpose of the trip, to talk to him ("this guy"). The DA's office was the one that set up the meeting, so someone from the DA's office was going to meet Monk et al, but that's not who they were going to talk to.
Mr. Monk and the Red Herring - S3-E10
Corrected entry: The guy who put the moonrock into Julie's tank replaced it with an exact replica, but he was never alone with the moonrock long enough to make a replica.
Correction: You don't have to be alone with a rock to make a replica! A good set of photos will do the job just as well.
Mr. Monk and the Panic Room - S3-E2
Corrected entry: After Monk has accidentally pushed the close button on the panic room door, Captain Stottlemeyer tries to guide Monk to pushing the open button on the wall. After a couple of minutes the captain puts his hand through the hole to open the door. The scene doesn't make sense, however. Stottlemeyer makes no attempt through the whole scene to try and open the door up for Monk, who is having trouble with the locked room. He can see the buttons and would easily be able to see he could reach it or at least try to reach it.
Mr. Monk vs. the Cobra - S3-E11
Corrected entry: In this episode Monk says that he never goes barefoot, but this is contradicted by an earlier episode, Mr. Monk Gets Fired. In this episode, Monk, after solving the case was 'doing a jig' and for the entirety of this scene he was barefoot.
Correction: When Monk was barefoot in the 'doing a jig' scene, he was distraught over losing his job and even more distraught over getting a new one. His mind was obviously miles away so he could be expected to have forgotten that he hates going barefoot.
Correction: The teacher was in on it. She pretended not to see the "victim" so Sharona would think she was going crazy.