The 2 EMS persons who rush in at MIT were not extras but were there for medical coverage for the actors from Boston EMS, which only cover the City of Boston. Unless they are going to help with a police action, bomb incident or warrant serving.
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Just before the scene where Jimmy claims to have contacted Interpol, a newspaper is shown with the headline "Dichotomy evident as NOW meets in Boston". This appeared in 2 July 1993 Boston Globe.
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The building where Max was "Blown Away" is now condos in Charlestown. Was originally a Catholic school which was closed in a cutback by the Archdiocese of Boston.
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The pair of claws that Tommy Lee Jones refers to in the beach scene is from "The Love Song of J. Alfred Prufrock" by T.S. Eliot.
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Boston's City Hall was used for the exterior shots for Police Headquarters. At the time of filming, BPHQ was located at 350 Stuart St., roughly a block from the John Hancock Tower. City Hall is 1 City Hall Square, essentially between Fanueil Hall (to the East) and 1 Center Plaza (to the West).
*There is a scene where a copy of the Boston Globe is seen with an article reading "2 More Bomb Squad Officers Killed in Mystery Blast". Behind it you can see the Business section with a headline "Bay State Bankruptcy Filings...". This article appeared in the 1 July 1993 Boston Globe.
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Loyd Catlett, who plays Bama, is Jeff Bridges' stand-in/stunt double in this film and in several other films.
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The second Tommy lee Jones bombing near Trinity Church is only a few blocks from the Boston Marathon bombing site . Life imitating art. .
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Spoilers
The trivia item below may give away important plot points.
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The statue of the man with the arrows embedded in him, which Gaerity dresses Max up as, is Saint Sebastian.