Continuity mistake: As the detectives are talking to their captain about the bank robbery, in a shot from behind the captain he takes his hands off his food and clasps them in front of him. The shot cuts to his front as he starts talking, and he moves his hands and clasps them again.
Continuity mistake: In episode 2.09 of related show "Arrow," during the day the particle accelerator is activated, Barry spends his time with Oliver, Felicity, and Diggle in Starling City. He arrives back in Central City just in time to see the particle accelerator activated, and he is in his lab because he was too late and missed the line at S.T.A.R. Labs. In episode 101 of "The Flash," Barry was never in Starling City during the day the particle accelerator was activated, and he and Iris actually attended the event. (00:02:10 - 00:11:30)
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.
Plot hole: During the fight at sundown, Cold gets a hit on Flash and he goes down. Eddie takes a shield and goes to help. But Flash was in the middle of the street with no obstacles around, and it's implausible that Eddie could have gotten to him without Cold or Heat seeing him.
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).
Deliberate mistake: When Capt. Cold is about to shoot Joe in the train station, Eddy "shoots" a pillar next to him to make him run. Eddy then comes from behind the pillar that got shot with no cuts. He would have had to been on the complete opposite side to shoot the pillar where it was hit. (00:32:50)