After Monk and the others first meet Dale the Whale, they go see a judge. Then, Monk is placing jelly beans on a scale. When the scene starts there are 4 beans. Monk places 6 more beans, and when he is placing the 7th making a total of 11, the close-up shows only 6 jelly beans.
When he's being forced to drink lemonade, the girl fills the glass half full. When he begins drinking it, it's only 1/4 full.
In S1, during the title sequences, Monk is shown getting ready for his day. The jacket he selects from his closet is gray, but the jacket he's wearing as he leaves his residence is brown.
At the beginning, when Sharona is talking about the Clue game, she describes it as "this woman, found murdered in her dining room with a rope." In Clue, the victim is a man named Mr. Boddy.
However, Sharon is essentially making up a false case and any details are basically improvised. The content of the game is irrelevant.
When the police officer brings the two chairs from the judge's house to Biederbeck's mansion, the pre-cut sections on the chair that the heavier officer stands on are obvious.
The girls force Monk to buy lemonade, but not to drink any. Monk is shown repeatedly drinking the germ-contaminated lemonade, yet he never paid for it. This defeats the whole "buy" purpose because the girls wanted money.
Dr. Vezza couldn't have been 37 in 2002. He claimed that he was conceived during the great Northeast Blackout of 1965. However, the blackout occurred in November of that year, meaning that he would have been born in 1966, and therefore making him 36 in 2002 unless he was mistaken about the circumstances of his conception.