Raylan says to Dewey that the Kentucky State Prison is in Manchester. It is not. The Kentucky State Reformatory is located in LaGrange, just to the east of Louisville.
The text of the newspaper article about the burglaries contains the same paragraphs repeated over and over.
When Raylan visits Boyd in the hospital, the pillow says "Lexington Detention," suggesting he's in Lexington, KY. However, Lexington is a full 3 hours from Harlan whereas the nearest trauma center to Harlan would be Knoxville, Tennessee, which is only 60 miles away.
In conversation with Dewey Crowe (Damon Herriman), Marshal Raylan Givens (Timothy Olyphant) states that Wyatt Earp deputized his guys right before the OK Corral, to which Dewey replied that they all died. Actually, Virgil and Morgan Earp along with Doc Holliday were all wounded in that shootout, but none of them died. This may not have been a script error, but Dewey Crowe's incorrect version of events at the OK Corral.