The Last Temptation of Barry Allen, Pt. 2 - S6-E8
Deliberate mistake: There's an awkward moment during Cecile and Kamilla's escape from Bloodwork's minions where Cecile doesn't close the door for several seconds so the cameraman can walk through as they follow them.
Mercy Moment Murder Measure - S1-E7
Deliberate mistake: When Abraham throws the secret note into the fire, he crumples it up before tossing it in. But then we see a shot of the note lying open and flat on the log before burning. Not only would the note not be able to uncrumple itself, it shows no sign of being crumpled in the first place. This was obviously done deliberately so the audience could read the note one last time.
The Campground 'Bizarre' Case - S1-E17
Deliberate mistake: The evidence that proves Kindaichi's alibi is the store receipt detailing the time of his purchase. Notice that the year is recorded too, but it reads "20XY." (00:12:40)