Crisis on Earth-X, Part 2 - S6-E8
Deliberate mistake: During the big battle, Arrow is knocked down and when he opens his eyes, the reflection in his eyes is tilted over to give the sense he's seeing things sideways. But the reflection should still have shown the proper orientation no matter what orientation his eye was at. Think of looking into a mirror and then rotating the mirror to the side, the reflection wouldn't rotate.
Winterfest - S10-E9
Deliberate mistake: Even though it's supposed to be Christmas time, the trees are lush with green leaves, no breath is visible when the actors talk and in the background you can see people wearing shorts and T-shirts.