Monk doesn't say his standard phrase "Here's what happened", to explain the sequence of events surrounding a murder. Instead, he tells Natalie, "OK I have a theory. It's completely crazy, but it would explain everything".
During the dinner sequence when they are showing the pictures on the screen, a picture of Adrian and Trudy is shown. A woman identifies Trudy but can't remember Adrian's name. Natalie leans over and says, "It's Adrian." The woman says, "No, that's not it. It's Anthony, I think." This is an obvious reference to the actor playing Adrian Monk, Anthony (Tony) Shalhoub.
Mischief Night: possibly a puzzling reference here to some British viewers (especially in the north of England), as here it takes place on 4 November, the night before Bonfire Night / Guy Fawkes' Night, not celebrated in the USA. (It appears from context to have a different, American usage.) Sometimes the mischief involves attempts by determined children to sneak around nicking the neighbours' wooden gates, fences, log-piles, and anything else inflammable to add to their bonfires for the following evening's celebrations.
One of the class members Monk first talks to (Todd, played by Reginald VelJohnson) played Sgt Al Powell in Die Hard and Die Hard 2. Another Die Hard character had a part in this season too: in "Mr. Monk Can't See a Thing (2006)," Art Evans played Rusty (the victim) who played Barnes in Die Hard 2.