Leland Stottlemeyer and Randy Disher (named Randy Deacon in the pilot episode) were named for Inspector Lestrade in the Sherlock Holmes series. Take the first two letters of their names (LEland STottlemeyer, RAndy DEacon), and they spell LESTRADE. See more...
Updates: 
Series 4 
Series 1, 2, 3, 5
Continuity: After Monk has been found in the coffin, Natalie and the captain comment on his smiling and the camera shows the candle has melted down all over Monk's hand. Then when the camera comes in closer, the candle is whole again and monk's expression has changed a little from the previous shot.
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