Factual error: The events of the first season take place in 1962, however, the JAG lawyer representing Sergeant Jenkins wears the Vietnam Service ribbon, authorized in 1965, and the Vietnam Campaign Ribbon, authorized in 1964.
The Marathon - S4-E3
Plot hole: Jason cheated in three different ways in order to beat Aurelius in The Marathon, and admitted it. So the bet that they made between them is null and void. But the last shot shows them living up to the terms, which includes Aurelius starting to eat his own shit (literally), so revolted that he's trembling. Apparently the writers really really wanted to include coprophagy. But who would eat faeces for a bet, if you can simply avoid it by reminding your opponent that he cheated? Or even better, many would say that cheating means losing automatically, so he's the one who should be eating his own shit.
Continuity mistake: Sometimes Cyborg is waterproof and sometimes he isn't.
Slouching Towards Bethlehem - S2-E8
Revealing mistake: When Kenya is being held at gunpoint the pistol pointed at her has a visible seam running up the grip and the back of the slide. It's a plastic prop.
Continuity mistake: The graffiti over the shutters is constantly different between episodes.
Factual error: In the scene where Bonnie gives Clyde the unloaded pistol through the jail bars, that gun was not manufactured until after 1972. It is a Bauer .25 ACP semi-automatic stainless steel pistol. Bonnie and Clyde's reign of lawlessness ranged from 1931 to 1934.
Factual error: The FBI agent introduces himself and says "Mike Weston - I did my thesis on Joe Carol at the academy." FBI agents are required to have a university degree, but they don't write thesis' at the academy. A person is either in a university or at Quantico getting trained. They are not writing papers at Quantico. They need the degree beforehand to get in. (00:10:30 - 00:11:30)