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)
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)
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: 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".
Deliberate mistake: When Joey and Jonathan get in Joey's car at Metropolis (just before heading to the police station), the car has headrests. When they get to the police station, see Lance Gessler leaving and then follow him, the car no longer has headrests. Obviously removed so as not to obstruct the actors.
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.