When Monk and Natalie are having lunch at her parent's house in the back yard, their seating arrangements change back and forth. In the close-up shots, Monk and Natalie are seated close together, as are her parents across the table. In the long shots, everyone is seated with equal distance apart - that is, they are seated in the 3, 6, 9, and 12 o'clock positions around the table.
When Monk is adjusting the chandelier, there is a quick cut to Mrs. Murphy and Monk is fixing the silverware on the table. When there is a cut back to Monk, he is fixing the chandelier.
When Natalie is telling Monk how she suspects that Paul either beat up her boyfriend or hired someone to, there is a cut shot from outside the passenger seat window where Monk was sitting. He's clearly not there. Natalie talks to an empty seat for a few seconds, and even gestures through where Monk should have been, and then he's back in the next shot.
Monk finds that the previous butler clipped the word "police" from a magazine by comparing the cut-out part with a burned scrap of paper he found in the fireplace. He matches them up, but there are several points at which the burned scrap extends beyond the clipped-out section, which is not possible if that's the source of the scrap.
When Natalie is leaving the luncheon, she brakes to avoid hitting Paul. A camera shot through the windshield shows her car was in Park (you can see the gear select lever) when she "braked."
When Paul Buchanan shoots the first butler, he clearly overshoots his mark - the gun is pointing half a meter away from the target.
[17:30] When Monk is speaking with the maid in his bedroom, she is standing in the doorway. Her reflection is visible in the mirror to her right. As Monk moves to his right and is no longer blocking the mirror, the reflection in the mirror of the floor shows a taped "X" spike indicating where the maid should stand for the scene.
[31:41] To give the appearance of the mansion location being larger, a cyclorama drop-cloth, creased and poorly hung, can be clearly seen in the hallway next to the dining room.
[31:41] As Natalie asks Monk to help her with her coat, they step into the hall. There is a crew-person clearly visible standing just behind them against the wall.
Monk's obsessive demand for order and cleanliness (including spotting a tiny, invisible-to-everyone else smudge in a glass) does not extend to the dirty mirror in his own room. He looks at it, but continues on just as if it isn't covered in large, very visible smudges.