The song that Ben Wade sings, "they're gonna hang me in the morning..." is called The Arizona Killer, and dates from 1995. It is a version of an older song, The Tennessee Killer, but even the older version is unknown before 1942.
There are dialogue references to "gunslingers", a term which did not exist until the 1920s. At the time of the film, such men would have been referred to as "shootists", "pistoleers", or simply "gunmen".
The construction sites in Contention have dimensional lumber being used and that didn't come into widespread use until mid 20th century. As explained in the behind-the-scenes featurette, the filmmakers decided to use the unfinished buildings in the final chase sequence because they ran out of budget for set-building.
In the saloon with Wade & his gang for a victory drink: When Wades gang leaves and Wade is taking his final drink at the bar with just the bar maid there, you can see he is taking the shot from a modern day plastic disposable shot glass, yet when he sets it on the bar it makes the sound of a glass shot glass.
At the end of the movie when the train finally shows up at the station you hear the bell on it ringing. But when it cuts to the train pulling into the station you can see the bell on top of it not moving while the sound of it is still going.
The first night camping out, Ben is sitting in the cold night air with just his shirt and vest on. The next morning he is again wearing his jacket. This is rather difficult to explain since he was supposedly handcuffed throughout the night.
In the fight with the railroad workers, one of the workers has a badge on the left lapel of his coat. When they are shown meeting Wade's gang in the tunnel, the badge is on his right lapel. When he is shot, it is again on his left lapel.
At the beginning, when Dan's son William lights a match to see at night, the match burns very slowly and irregularly, varying the burnt length. When he puts it out, only the tip is burnt despite it being lit for about 60 seconds.
After the stage coach tips over Charlie Prince goes over and picks up Byron McElroy's shotgun, he breaks it open to check it. The scene then starts from another angle still showing Charlie Prince and he breaks the shotgun open a second time.
When the stage coach is being ambushed, one of the men in the back shoots one of the gang members and is hit on his left ear. As they arrive in town, they signal each other to go to the tavern and you can see that the man hurt on his ear is no longer hurt on the left ear but instead is hurt on his right ear.
During the exchange of Ben Wade with the deputy in the stuck coach in front of Dan Evans' Ranch, you hear the Marshall cock his revolver just before Ben Wade is let out. In the subsequent shot his revolver is not cocked.
Bisbee, Arizona is portrayed as being laid out on a flat plot of land, when it is actually a mountainous, hilly town. The general appearance of the countryside shown in the film bears scant resemblance to southern Arizona, where this movie is set.
In the shots at the train station you can clearly see all of the land in the background is covered in snow. There's even snow on the tracks. Not only is it evident that it's spring or summer time but there is a drought. Even though Contention is a distance away from Bisbee there would have never been a drought at one town while there's a blizzard at another.
Anesthesia had been in use for over 25 years before 1880. But it was still expensive and difficult to get, especially in distant towns. Furthermore, though Doc Potter is a very organized doctor, it is indicated that for a long time, most of his patients have been animals. And while the preservation of livestock and service animals was important enough to take pains to take care of them, anesthesia would not have been considered necessary for them (in the days before the ASPCA, it would have been considered an impractical waste.) Therefore, it is logical to assume that Doc Potter, having had few or no human patients in recent memory, would not have any readily available. It is also likely that McElroy would have refused it, anyway.
Dan tells his wife that he 'has been standing on one leg for three years.' This is metaphorical, and a play on words at his own expense. He is referring to how long he has been trying, unsuccessfully, to maintain the farm and support his family in the Arizona territory. He is not referring to how many years have past since he lost his leg in the Civil War; the screenplay clearly states that the film is set in 1884.
At the hotel, Butterfield slides a badge under the hotel door, yet after the door is opened the sheriff and his deputies are all wearing badges. However, the badge Butterfield slides under the door is a deputy badge for Dan, hence Dan throwing it back to the sheriff when he leaves.
The outlaws are after a stagecoach which they know carries a Gatling gun. They have cleverly set up a way to stop it - but decide for no good reason to first chase it and get shot at, with predictable losses.
SPOILER. In one scene, Wade is pointing a shotgun at Evans, Doc and others. Evans' son sneaks up behind Wade, aims at Wade's head, and demands Wade drop the shotgun. When Wade hesitates, Evans' son fires a warning shot just to the right of his head. When the shot changes to a perspective behind the son, you can see that the warning shot he just fired just to the right of Wade's head would have probably hit Doc, Doc's horse, Evans, or one of the other good guys - they were standing just to Wade's right.
Before the gang set the stage coach on fire, one upward-angled shot of Charlie Prince shows that there is no roof on the stage. The lawman "trapped" inside could have exited through the large rectangular hole at any time.
When Wade, Dan, and the group are escaping through the tunnels after Doc hits the man with the shovel, Doc gets shot in the back but there is no bullet hole in his jacket. You can see the blood from the front when he dies.
After Byron is shot in the stomach, he is taken to a doctor for emergency care. But rather than having a simple bleeding hole where the bullet penetrated, his stomach is completely torn open. This type of extreme trauma is inconsistent with a single bullet entry wound.
The goof item below may give away important plot points.
Unless the 3:10 was more than "running a little late" there seems to be a significant loss of daylight in the final scene. As we watch the final shots of the train leaving town and son standing over his father's body, the sun is seen in its last light of the day; lighting both the underside of train and 10 gallon hat. However, at its shortest time of the year, the sun doesn't set on the Arizona region until well past 5pm.
In the Climactic sequence, while Ben Wade still has his back to his gang, the Mexican Marksman tosses Wade's gun to Charlie Prince. Moments later another gang member arrives with the gun and passes to the Mexican who tosses it to Prince again.