Continuity mistake: When Ellerby attacks the guy for not installing the cameras in the right place, he knocks off a map from the board. A second later Ellerby is still going after him, and the map is fixed.

The Departed (2006)
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Directed by: Martin Scorsese
Starring: Alec Baldwin, Mark Wahlberg, Matt Damon, Jack Nicholson, Leonardo DiCaprio, Martin Sheen
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Surveillance Guy: Who the fuck are you?
Dignam: I'm the guy who does his job. You must be the other guy.
Trivia: This was Martin Scorsese's first film to win Best Picture. And his first Oscar for best Director. Martin also said that this was the first movie he ever made with a plot.
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Answer: The FBI and police are separate organizations that do not share full information. Only the FBI and Costello himself knew about the informing, and the FBI can only do so much to stop Costello being caught without drawing attention to their relationship. The police and Costello's gang are fighting a separate battle, hence the two moles.