Continuity mistake: In "Mr. Monk and the Birds and the Bees" Natalie mentions she doesn't have a sister when Julie's "boyfriend" says the aunt hired him to break her and her real boyfriend up. Here she has a sister and a niece.
Suggested correction: Natalie doesn't have a sister in this episode. The woman seen is credited as "Aunt Teresa." They're most likely cousins. Children of cousins are often referred to as nieces/nephews. This would make Natalie "Aunt Natalie" to Anne Marie (and Teresa would be "Aunt Teresa" to Julie).
Continuity mistake: When Monk comes home (after being at Steve's house) and starts to pet the dog, the dog sits down. But in one shot she's suddenly standing and wagging her tail, but then back to sitting in the next shot.
Continuity mistake: When Monk takes the dog to the park, they're standing on the curb by the grass when he goes to take the leash off. After he says "get ready", the shot changes and they're not by the curb anymore. They're back on in the next shot.