Eyewitness - S1-E12
Continuity mistake: When the immortal who's trying to kill Tessa snipes at her in Duncan's car, his shot shatters the passenger-side window. When Duncan tails Tessa and her police escort to the safehouse, the passenger-side window is intact. (00:30:05 - 00:35:50)
Heart of Ice - S1-E3
Continuity mistake: When Mr. Freeze's henchman Johnny gets his legs frozen, he is wearing pants and shoes. Later when Johnny is inside a water tank in the Batcave in order to thaw the ice, he has been stripped down to his boxer shorts. While it's possible for Batman to remove Johnny's pants above the freeze-line by cutting them away, he would still have remnants of his pants underneath the ice, but when the ice is thawed, his legs and feet are bare. (00:05:45 - 00:08:05)