Factual error: When Walter Goggins fires a LAW at the church from next to the vehicle, the back-blast from the rocket would have shattered the car's windows, and flying glass fragments would likely have injured the occupant. The show depicts neither outcome.
The Hammer - S1-E10
Character mistake: Raylan Givens tells Judge Reardon that he carries a ".45 Glock" but this is untrue. Throughout the series with the exception of the beginning of the first episode Raylan Givens carries a Glock 17, which is only chambered in 9mm parabellum. His backup can be seen to be a Glock 26 which is also in 9mm.
Raylan Givens: If you're going to talk, I'll put you in the trunk and drive myself.
Dewey Crowe: I can't drive handcuffed to the damned steering wheel!
Raylan Givens: You'll get the hang of it.
Whistle Past the Graveyard - S5-E8
Question: Boyd and crew nearly ruin their relationship with Yoon by killing the Memphis crew in Mexico, as they were warned not to kill anyone south of the border. They redeem themselves by saying they'll take care of the bodies themselves and get them into the US. All well and good until the Mexico police stop them, and the crew let them take the truck with the bodies, congratulating themselves on the deception...but how does that solve anything? Corrupt or not, the cops now have the bodies, in Mexico.