Mr. Monk Visits a Farm - S5-E14
Character mistake: When Randy Disher is having Chinese food in his apartment with his new girlfriend in 3-12 "Mr. Monk Gets Cabin Fever", he gets a fortune stating that he is going to get money from his uncle, and says that he doesn't have an uncle. In this episode Randy inherits a farm from his uncle who appears to have committed suicide, but was actually murdered.
Suggested correction: Randy says when that uncle dies that they were never close, so his leaving him the farm comes as a total surprise. It's still a character mistake, however, Randy is established as the sort of person who could "blank out" a relative that long-lost.
Randy says he can run the farm because he went there and helped his uncle every summer.
Broken Souls - S6-E2
Character mistake: At the very end of the episode, a chess board is set up wrong, the initial position must have the white queen on the white square (d1) and the black queen on the black (in this case red) square (d8). They set up all the other pieces correctly except the kings and queens should be reversed.
Character mistake: Horatio writes the symbols for sulfuric acid, H2SO4, on a clear board. Both numbers should be subscripts but he writes the 4 as a coefficient (which precedes the name of the acid but he writes it after), suggesting a lack of basic chemistry knowledge.
Unto Others - S4-E7
Character mistake: When Cutty quits the truant officer job and walks out of the office, he runs into his old girl from way back. She calls him David instead of Dennis. (00:51:00)