Deliberate mistake: The first 10 episodes of Season 5 were shot in a totally different order than they were aired. As a result, Jamie's size during her pregnancy is very inconsistent at the beginning of the season. In particular, she gets much smaller between episode 8 and episode 9 because episode 9 was originally supposed to air earlier in the season.
Deliberate mistake: At the end, a line apparently cut earlier creates slight confusion. Nick says to Nat, "When LaCroix asked you why?" (why save vampires). In the earlier scene as shown, the elusive LaCroix spoke only briefly to Nat in the lab, and never asked her that question. (00:42:20)
The Lotus and the Steel - S4-E13
Deliberate mistake: Every native of the Japanese village that Wolverine visits is conveniently fluent in English, and they even speak English to each other when no other people from English-speaking countries are around. (00:04:45 - 00:20:45)
Deliberate mistake: The judge grants wheelchair bound Hilda Mars a million dollar settlement for her injuries. Then Sydney confronts her outside and wrestles her up out of the chair in which Hilda fakes a tumble down the steps. That night Hilda's attorney visits Sydney and admits he knows Hilda is a con who got away it instead of calling it out to the judge.
Deliberate mistake: At Pete's diner, the owner puts the tray down, and instantly glasses appear in front of the 5 patrons. (00:02:50)