Revealing mistake: Costigan carries a Walther PPK/S. The hammer on his pistol is down both before and after he shoots the junkie armored car thief. The shot to the leg should have automatically recocked the hammer.
Character mistake: During the funeral at the end before the 21 gun salute, the NCOIC called for "half left face", that would cause everyone to get shot in the face.
Suggested correction: Half-left face means a 45° left turn (left face is a 90° turn), so wouldn't result in anyone getting shot.