Mr. Monk and the Three Pies - S2-E11
Factual error: In this episode, when Sharona and Monk arrive to visit his brother, they talk about the swing set. Monk tells Sharona that his father put up the swing when he was 8 years old but this is a much newer swing set. Look at the curved plastic seats: these have come about in the last six to eight years. It also doesn't look at all rusty like a 40 year old swing would.
Suggested correction: Ambrose is obsessed with leaving the place "exactly the way dad left it for when he comes back." Hoarding old newspapers for him would be a character mistake, but things like keeping the old swingset maintained and up to current safety regulations so everything's perfect "when he returns" would be a thing he'd find to do around the house. His agoraphobia might not be so bad in the yard. Alternately, he could pay someone for yard upkeep, which would include the swingset.
Mr. Monk and the Three Pies - S2-E11
Continuity mistake: When Van Rankin takes the borrowed flour from his kitchen counter and hands it to Sharona, it's in a standard paper flour sack, and the counter is clean. Later, there's flour dust on the counter and the impression of a large, round flour tin - like the one in Monk's kitchen - instead of an imprint of the paper sack. (00:37:20)
Mr. Monk and the Three Pies - S2-E11
Continuity mistake: When Van Rankin shoots his wife, the black gym bag, which has been slung over his shoulder since he entered the kitchen, disappears between shots. (00:31:05)