Continuity mistake: As Barry is going up the stairs in the police station and says he doesn't want a museum dedicated to him, a man and a woman are walking down the stairs. However, a second later, the shot has changed and the man is now a different person and the woman has gone completely.
Other mistake: When Cisco and Cailtin call Barry to tell him about the man with the gun, Cailtin says he has a gun. Cut to the cops pursuing him, the perp shoots at the cops, and one of them seems surprised that he has a gun. There's no way Caitlin could have known about the gun without the cop knowing (which would presumably have been relayed over police communications).