Deliberate mistake: Early on, The Flash's immense speed caused his clothes, and those of people he was carrying, to catch fire because of the air resistance. Gave him an excuse for the suit, but this effect was fairly quickly forgotten, with him frequently carrying civilians or running out of costume with no ill effects at all.
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)