In the whore house scene where the towns people mistakenly shoot the sheriff, Billy explains in voice-over that he was blamed for that killing though he never even fired a shot. This is an error as Billy clearly fires the first shot as he pushes the sheriff out of the front door inciting the towns people to open fire on who they think is Chavez the Indian.
After his capture, when Billy is in the room with Deputy Bell, there is a knock on the door, Deputy Bell cocks his Winchester, putting the hammer back in the firing position. When the door opens, the Madam, Jane Greathouse, is standing there, Bell has the Winchester at his shoulder and the hammer is in the down, or fired position.
In the scene where the gang is surround by Garrett's men and Doc is shot, Arkansas Dave Rudabaugh is seen standing straight against the wall holding both guns up, after Billy hands Doc a second gun, Arkansas Dave Rudabaugh can be seen crouched with the right hand gun parallel to his side. In the next shot he is standing against the wall again with the guns held up.
In the White Oaks whorehouse, just as Billy agrees to send an Indian out to satisfy the crowd, we see Dave getting up from the table. In the very next shot Dave is stood next to the Sheriff, tapping him on the shoulder.
Shortly before Tom O'Folliard gets shot, Billy states "we'll have a clear view of the Nachita River. We'll sell the horses off, and then we'll take a skiff downriver into Mexico." There are no rivers in New Mexico, besides the Rio Grande and Pecos [Pecos flows through several hundred miles of Texas first], that flow towards Mexico, and, in fact, there is no Nachita River.
The land border between New Mexico and the nation of Mexico is a mountainous region with a few flat plains with no rivers and only tiny streams. If the gang was seeking to flee into Mexico there would have been no natural physical barriers to stop them and the crossing could be accomplished within minutes.
When Billy and the gang are talking to John Chisum the actor playing him, James Coburn, has a generous application of fake tan on his face (This is common in Hollywood and done to make older actors look younger). As the wind is in his face his hair is blown back and you can clearly see his normal skin color and the fake tan 'line'.
When Arkansas Dave and Chavez fight over the burial ground, Chavez is laying on his back with his arm up and Dave stabs him through the back of his arm. When Chavez asks if he wants his knife back, they are both standing up and Dave pulls the knife out from the opposite site of the knife entrance.