When Raylan is being escorted into the back of the cop car, the arresting officer takes the Stetson off and puts it on top of the car. After the officer gets in the driver's side, the Stetson disappears. Later, when Art gets Raylan from the arresting officer and he gets in the back of the Marshal's vehicle, Raylan is wearing the Stetson again (it magically reappears).
In the barn shootout, Boyd empties his Beretta 92FS and then pulls the trigger twice while aiming it at Eva. He also mentions to Raylan that his gun has no bullets. The slide on a Beretta 92FS will lock in the open position when the last round is fired.
The goof item below may give away important plot points.
There are multiple problems with the Oklahoma driver's license that Raylan tells Boyd belonged to Ava. First, it states it was issued in 2005 yet expired in 2017. Oklahoma driver's licenses expire every four years. Secondly, it lists the date of expiration as May 25. Oklahoma driver's licenses expire the last day of the month first issued. Thirdly, it lists her address as 0232 Cedar Way instead of 232 Cedar Way. Finally, and most noticeably, the abbreviation for her eye color is shown as "BND" which makes no sense as an eye color. It should be BLU (blue), BRO (brown), GRN (green) etc. Someone as slick as Boyd might quickly deduce that was not a "real" fake license that Ava could have used to successfully evade the authorities for so long.
The text from the newspaper clipping with the photo of Ava is problematic, including a lede that does not make sense and then the same lede text (shown without the mistake) starting over several paragraphs later.