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.
Deliberate mistake: The "chest compressions" Diggle performs on Oliver at the beginning of this episode are laughable. He's barely applying any pressure at all, and his arms are almost straight out in front of him instead of straight down. I would have called this a character mistake since Diggle really ought to know better, but this is more of a safety issue than an oversight; real chest compressions tend to break ribs.
Deliberate mistake: Whenever Deathstroke is on screen, he has three grenades for a launcher strapped to his chest. But on closer inspection, you can see these grenades are actually BB-gun grenades: You can tell by the very distinctive holes at the tip. They did this because launched grenades are A) very expensive and B) not very safe to walk around with on set. A few of the most noticeable times are when Yao Fei is fighting him when he is freeing Oliver in episode 5 and when Oliver is talking to him in episode 14.