When Monk and Sharona are first getting on the plane, we see a balding, bespectacled, man wearing an orange/brown coat getting on the plane just before them. This is Andy Breckman, the show's creator. See more...
Updates: 
Series 2
Continuity: As Stottlemeyer steps off the stage, after singing, he is holding the microphone and pulls it down so that the top is pointed toward the floor but in shots following this, when he is talking to the woman, the microphone is back in an upright position.
Continuity: After Monk tells Randy to hit whilst playing Blackjack, the dealer gives him the Three of Spades. The dealer places it a bit to the right and over the Eight of Spades. The next shot we see of the cards the Three is now completely over the Eight and we can only see a bit of the bottom of the Eight.
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