Continuity mistake: When the police are moving in to arrest Dzhokhar Tsarnaev, the shot shows an FBI SWAT officer grabbing him. But in the next cut, the officer changes to a Boston Police Officer while changing back to a FBI Officer in the following shot.
Other mistake: In the Watertown police shootout scene, a resident tosses a sledgehammer to the police to help them in the fight. Right when the resident throws the sledgehammer from their front door, many frames are entirely missing from the movie for some reason, which results in an awkward skip. This is seen in all cuts of the film (Blu-Ray, Digital, etc).
Continuity mistake: Sgt. Saunders wears his duty belt throughout the movie with his radio on the right and gun on the left. When Sgt. Saunders enters the Black Falcon Terminal and says "Whatever it is, I didn't do it," his gun is now on the right and radio on the left. (00:51:05)
Continuity mistake: In a scene early in the movie a gas station sign shows the price for gas at $2.13. The next day another gas station is displaying $3.19. Gas was actually $3.40+ at the time of the actual bombing.