Continuity: When Alice is in Stottlemeyer's office and Stottlemeyer can't find Terry's present, Alice says, "But what about..." indicates the bottle of port, and then drops her arms to her sides. In the next shot (when we see Alice from the back), we can tell by the position of her elbows that her hands are not at her sides, but in front of her.
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Trivia
In "Mr. Monk and the Airplane," the flight attendant he keeps irritating is Tony Shalhoub's real life wife, Brooke Adams. See more...
Updates: 
Series 2
Mr. Monk and the Secret Santa (season 4, episode 9)
Continuity: When Alice confesses to the murder in her kitchen, a large green plastic bowl that's been sitting on the counter disappears between shots.
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