In the beginning of the episode, Linda Kloster states that her husband's IQ is 180, 4 points higher than Albert Einstein's. Although experts estimate Einstein's IQ was somewhere between 160 and 180, he never officially took an IQ test so his actual IQ is unknown.
While Adrian, Natalie, and Julie are watching the chess game in the park, a close-up of the game board shows the black Queen has the white King in check. The white player (Tovalah) does nothing about it (he captures another piece) and the man playing black simply resigns and walks away.
During the stakeout, Natalie starts to take a sip from the lemonade cup with the drink in her left hand. The shot the changes to the other side of the car and Natalie is in the middle of her sip, but the cup is in her right hand.
When Monk is talking to the two mourners he mistakes as being the victim's aunts, Natalie is in the background behind the two elderly women. The camera angle switches to show Monk, and when it switches back to the mourners, Natalie has vanished from the background, and the next angle change shows her standing a few feet away from Monk.