Continuity mistake: Ava spills Coke on her blouse and creates a big circular stain. As she walks to the bathroom, the stain becomes a long narrow one. When she is leaving the pizza place, the stain is still narrow, but much shorter. (00:21:00 - 00:22:00)
Continuity mistake: In the scene with the horse trainer, the character has a wedding ring on, then doesn't, then does, and finally doesn't again. (00:30:40 - 00:32:50)
Continuity mistake: The first time Boyd speaks with Ava's uncle Zachariah, the door behind Zachariah keeps switching between open and closed between shots.
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.
When the Guns Come Out - S3-E6
Plot hole: Raylan has a hunch that Winona took the money again from the evidence room, so checks the locker, finds the empty box, and assumes she stole it. When they returned the money in the previous season, he said "Put it back anywhere except for where you found it", so as to make it easier for someone to assume it had been misplaced, rather than lost. So the locker being empty is hardly a smoking gun for him to assume Winona's taken the cash.
Truth and Consequences - S4-E3
Continuity mistake: As Eve is taken out of the closet you can see the luggage table or chair flipped over and just a few seconds later it's upright. (00:29:24)
Other mistake: Ava previously borrowed a razor from another inmate to tidy up her unevenly-hacked hair. All well and good, except especially when seen from behind her hair has been perfectly bobbed and tapered, hardly possible doing it herself in a prison bathroom with a razor.
Other mistake: Raylan fires two shots into the above-ground pool, but it springs three leaks. Looking closely it does appear that Timothy Olyphant squeezed the trigger three times, but one blank must have misfired, and the three squibs went off regardless.
Continuity mistake: As Raylan sits down opposite the thug, who says "I just take orders", his gun is held vertically. Cut to a shot from the front and it's on its side. (00:25:00)
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.
