Stumpy refers to the cleaned up Dude looking like "Mrs. Astor's pet horse." Even if Stumpy, as unlikely as it seems, knew anything about New York social circles, Mrs. Astor's spending habits were decidedly later than the time frame of this movie.
The majority of the men in the film are clean shaven. Given the 1885 setting of the film this would be statistically impossible to occur as most men in the Old West wore facial hair as it was in fashion and it was nearly impossible to shave frequently with limited access to clean water.
The clothing worn was clearly of modern manufacture. The buttons and seams were clearly machine-stitched in a time when most clothing was handmade. In addition, the hats worn by most of the cowboys are clearly the type worn in the 1900s ( at the earliest) and not the 1880s.
When Stumpy, Dude, and Colorado are sitting around playing music and singing, on the second song (where Stumpy sings) in the second verse, Colorado sings "I wish I had an needle..." but he mouths the words "I wish I was a needle."
When Dude comes back from parking Pat Wheeler's wagons, he tells Chance he's going to get a beer. Chance tells him there are some cold ones inside. When Dude is getting off his horse he says "Just as long as it's beer" yet his mouth never moves.
When Dude drops the $50 gold piece on the floor after shooting the bad guy in the loft, it makes a tinny sound when hitting the floor. A $50 gold piece was 2 1/2 ounces of gold and would make a distinct "thud" when hitting a wood floor.
The first line is Chance saying: "Joe, you're under arrest." However, he clearly begins talking before his voice is heard. He appears to say: "Come on Joe, you're under arrest", but those first two words have been silenced.
When Pat Wheeler has come into town, and is talking to Chance, different shots were done at obviously different times of day. When the camera is facing the jail, the sun is coming from the right... when facing back up the street, the sun is again coming from the right (the opposite direction).
After Chance is tripped on the staircase, he ends up lying on
his stomach with his arm partially under him. When they roll him over, to wake him up, he is lying more on his side, and his arm is now behind him.
After Chance is tripped on the staircase, Burdette's men roll him over and splash him with a bucket of water. The water stains/marks change numerous times between Chance getting up and walking to the jail.
Dude is attacked by four men and has his head and shoulders pushed into a horse trough. Just before he is grabbed he is leaning over the trough and his shoulders and upper sleeves are damp from a previous take.
When Wheeler first gets to town and is talking to Chance about everybody stopping him, Chance's right hand is alternately holding his rifle, or resting up on the Pommel of Wheeler's saddle. It changes a few times during the scene.
After they put Joe in jail, and Joe tells Dude he should sit back there in place of Stumpy, Dude is holding his beer bottle down by his hip. When the camera angle changes, Dude is holding the bottle up by his mouth, and then throws it at Joe.
When Dude stops Nathan Burdette and his men to have them put their guns on the fence, his position changes. Sometimes he's standing in the middle of the street and other times he's next to a hitching rail resting his hand on it.
While Colorado and Chance are talking just before Feathers throws the vase through the window, Colorado is rolling a cigarette. He places the tobacco in the paper in his left hand and doesn't seal the paper. In the next shot, he gestures with his left hand holding the unsealed paper, but no tobacco spills out.
After Dude is captured the first time, and Burdette's men ride up the street, the shadows change direction between shots of them approaching and Chance standing out in front of the Hotel with Colorado. These shots were obviously filmed at different times of day.
When Dude is jumped and dunked at the water trough, one of Burdette's men takes his hat and vest as a disguise. After Chance shoots that same guy dead at long distance he falls off his horse near the water trough. After Chance frees Dude, they can't find Dude's hat (and vest) and the dead guy that was wearing them has disappeared.
Toward the end of the film, when Dude is talking to John T. Chance about the girl 'Feathers', Dude says the Ft. Worth stage runs at night and 'Feathers' might be on that stage leaving town. 1880s Texas stages never ran at night.
Regarding Stumpy throwing sticks of dynamite and Sheriff Chance and Dude shooting them, Dynamite does not explode when hit by a bullet. It is a very stable medium that will only explode when a blasting cap (usually with a fuse inserted into it) explodes. Likewise one stick that is attached (or bundled) to others can set-off a chain-explosion as long as there is at least one blasting cap that explodes. Dynamite can be shot, struck, dropped, or even burned without exploding.
Colorado (Ricky Nelson) tells the sheriff (John Wayne) that he and Dude are the only ones who saw the shooting. The sheriff says they are only ones who are willing to testify. The sheriff was knocked out cold by Dude hitting him on the head before the shooting in the saloon. The sheriff is lying on the ground, not moving at all. Furthermore, he's lying on his stomach, on the floor and his back is facing the shooting done by Joe. He would be unable to see any of the events after he was hit over the head by Dude. Therefore, he could not testify in court about any aspect of the shooting. Even if he was awake and listening, but not moving, he would have heard very little because no one speaks in the saloon before, during, or after the shooting.
John T. Chance wears a wedding ring throughout the movie even though he was not a married man in the story. However, John Wayne was married at the time in real life, but did not take his ring off during filming.
Towards the beginning of the movie, Dude is shown at the end of town when the sun is rising. Later in the movie the same camera angle and view are used as a sunset shot of Dude before he returns to the jail.
When Feathers is sleeping by the bar with the shotgun, Chance comes from upstairs, picks her up, and takes her upstairs. He comes down starting from the first landing, without coming down the upper stairs or crossing the middle landing, which are both visible the entire time.
The goof items below may give away important plot points.
At the end of the film when Chance tosses Feathers' tights out the window and they're picked up by Stumpy, you notice that they're obviously elastic tights. Elastic didn't exist until well into the 20th century.
Towards the end of the movie, after Burdette and his men have surrendered, Colorado is leaning on a water barrel with his hand, and raises his cup to his mouth to drink. When the camera angle changes, he is now leaning on the barrel with his elbow, and his cup is held down by his waist.
During the exchange of Dude for Joe, when Dude comes off the stairs of the warehouse, the shadow is behind him. When the camera changes to Joe, his shadow is behind him too. That would be impossible as they were walking towards each other. These shots were done at different times of day.
When Chance is tripped Dude is in the bath, he walked in wearing a solid blue shirt, he looks out before the action starts bare-chested but when Chance is tripped he looks out the door and he's back in the blue shirt. Burdette's men then take him hostage, when the exchange is being made, him for Joe, Dude walks out of the warehouse in a brand new set of duds, a patterned shirt and a tan vest.
When Dude is fighting Joe, Colorado asks if he should help Dude. As he is talking, a bullet hits the right side of the window frame. A moment later, a cut back to the window shows no mark from the bullet.
When Dude shoots the gunman out of the loft in the saloon, the gunman lands right next to the glass on the bar that the blood was dripping into. This would be impossible since he fell forward out of the loft. Therefore the loft is not long enough for it to hang over the glass on the bar, and drip blood into it.