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)
Things You Can't Outrun - S1-E3
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.
Power Outage - S1-E7
Continuity mistake: Barry examines the charred corpse in the morning, telling Joe and Eddie he hopes they skipped breakfast. He goes to Star and Cisco does facial reconstruction. They get the alert about the power plant, and when Barry arrives, it's nighttime.
Fast Enough - S1-E23
Continuity mistake: When Eddie is dead, his eyes are closed. But in a close up shot of him, his eyes are opened. Then when he's being pulled into the wormhole, they're closed again.
Continuity mistake: At the facility test while Barry is about to run the sun changes between shots.
Fast Enough - S1-E23
Continuity mistake: When Ronnie and Caitlin are getting married the sun changes between shots.
Going Rogue - S1-E4
Continuity mistake: When Captain Cold shots Joe with the ice gun, he hits Flash instead, in the left side of his abs, but in the next shot the ice switches sides.