At the end, the Captain says that Monk has been put on retainer and guaranteed 16 homicides a year for 2 years. This is how long the series had been extended for at the time (32 episodes for seasons five and six).
The voice stress analyzer that Rufus wants to use is actually a PlayStation Portable aka PSP.
The plaque at the transcendental retreat referred to Jennie Mandeville as the "cherished founder and teacher" - the show's production company is Mandeville Films.
Monk refers to having to choose which of two identical cans of soup to put back as a "real Sophie's Choice," referencing Sophie's Choice (1982). A "Sophie's Choice" means a choice between two extremely difficult options, where both choices can have either equally positive _or_ equally negative outcomes. It's often misused to refer to making low-stakes choices where one outcome actually is better than the other, but in Monk's case, he likely really does find having to select one can over the other to be agonizing.
A man parks his motorcycle outside the museum while two detectives are talking. As he's getting off the bike, one of them says to him, "that's a handicap spot" to which he replies, "it's okay, I'm psychotic". This is a clear reference to Johnny Dangerously (1984) when Joe Piscopo says, "I am handicapped, I'm psychotic".