Continuity: In this episode Randy is allergic to cats, in fact he has an allergic reaction even if a cat has been there lately but is not there now. But in Mr. Monk and the Sleeping Suspect, during the scene where Monk and the police are investigating the woman's destroyed house, a cat passes within a few feet of Randy, who doesn't sneeze or show any signs of his allergy.
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Trivia
According to co-producer Tom Scharpling, the Mexican homicide cops are purposely written as parodies of Stottlemeyer and Disher, right down to their attitudes, their ranks, their suits, and Captain Alameda's mustache. Even the bumbling lieutenant's name is a little joke on Disher. Plato means "dish" in Spanish. See more...
Updates: 
Series 2
Mr. Monk and the Missing Granny (season 2, episode 13)
Factual error: The SFPD fails twice to trace the kidnapper's call because he isn't on the line long enough. This is an erroneous holdover from really old movies and the days before digital & computer technology. Phone calls have been instantaneously traceable since the 1970s. There's a line tossed in claiming that they need 45 seconds if it's a cell phone, but this is still bogus: cell phone calls are also instantly traceable.
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