It Happened 'That Night' - S3-E1
Character mistake: Emily's mom tells Emily that reporters were there to talk to them about "Emily's missing remains." It's supposed to be "Allison's missing remains." (00:17:00)
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.
Character mistake: Nathan suggests to Dwight and Audrey that maybe he should shut down the meeting of troubled people. As chief, he should know he has no authority to stop citizens from assembling.