On multiple occasions, Raylan and the Marshals become involved in criminal activities which would either be the jurisdiction of local and state law enforcement or some other branch of the Department of Justice.

Many times people shoot guns inside of cars and even right next to ears. Under those circumstances the sound is not only deafening but incredibly painful. No one ever reacts with pain or goes deaf.

It is clear from the surrounding countryside in more than a few episodes that while the series is set in SE Kentucky, it isn't filmed there. This includes scenes with treeless mountains in the background and semi-arid landscapes.

Ava's gunshot scar disappears. After Ava is shot in the shoulder, she has a bullet wound scar. But in the final season, she wears a strapless dress that exposes her shoulders. There is no longer a bullet wound scar.