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.
Walker: You shot me in the back!
Raylan Givens: You wanted to get shot in the front, you shoulda run toward me.
Question: Mags poisons herself with the same "it was in the glass, not the jar" approach she took with Loretta's father. But we see her grab two glasses - one from the cupboard and one off a shelf. Does she slip poison in while off camera, or is it just that the cupboard/shelf glasses are always poisoned, trusting that everyone knows not to use them? Seems like a crazy risk to take.