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)
Deliberate mistake: Whenever Dexter injects somebody with M99, they are immediately rendered unconscious. In reality, this would take several minutes.
Tall Woman in Red Wagon - S1-E6
Deliberate mistake: When the workers hit the coffin lid with the shovel, it is (obviously) fully buried and they moved just a little bit of soil off it. Rockford moves closer, and instantly the inside of the coffin is covered by the thinnest layer of dust, uniformly. (00:02:30)
Deliberate mistake: They show footage of Max and Larabee scouting out the entrance to a bank. This same footage was used in the earlier episode "The Treasure of C.Errol Madre".
Episode #1.3 - S1-E3
Deliberate mistake: When the judge shoots himself, the revolver slides across the table, to fake his murder by someone else. But there is no mechanism in place that explains how he does this, making it appear as if he is able to accurately throw/slide the gun after shooting himself. In the original novel, he used a rubber band to achieve the effect, but he is not shown setting it up here.
Genesis (2) - September 13, 1956 - S1-E2
Deliberate mistake: When Sam ejects and lands on the ground, the closeup is a flipped shot, note the "US Air Force" is backwards on Sam's helmet. (00:19:10)
Deliberate mistake: When Sam first meets Mickey (who is posing as a bank robber), Mickey says he needs Sam to state that he needs Mickey's help in robbing a bank, so if Sam turns out to be an undercover cop, Mickey can plead entrapment. This is a classic error. Entrapment only exists where a cop actively persuades a criminal to do something he otherwise wouldn't have done - which is not the case here. If Mickey as a con artist knows this (which is likely), it's a deliberate mistake, otherwise it's a factual error. (00:30:09)