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).
When Gaerity orders Guinness in the Irish bar, what he is served is more like lager (totally wrong color and consistency) yet this doesn't seem to faze him.
Position of Kate's Jeep at the beach house. Early on, we see her Jeep facing the water with the driver's side door closest to the beach house. Later, when Gaerity secures the latch on the hood, we see that the Jeep is facing away from the water and the driver's side is away from the beach house.