The song "You're In The Army Now" is played after a four-man team of cavalrymen drink contraband whiskey and end up in the guardhouse. This movie is set in 1874, but "You're In The Army Now" wasn't written until 1917.
Approximately one hour into the film, when Colonel Thursday and Captain York prepare to leave the fort to protect the wagon-team led by 2nd Lieutenant Michael O'Rourke from an anticipated Indian attack, the class-conscious Thursday criticizes York's soldiers for their sloppy uniforms, pointedly telling York himself that York's hat should be creased "like a fedora." The action of "Fort Apache" takes place during the lifetime of Cochise, the famous Apache chief who died in 1874. The word "fedora" does not enter the language until 1882, when the hat worn by Sarah Bernhardt as Princess Fedora in Victorien Sardou's hit play "Fedora" became the rage of the fashion world. Thursday's use of the word is an anachronism.
When the new recruits are assembled for the second time (in uniform) the two closest to the camera appear to be wearing denim jeans or Levis. Levis were not available to the U.S. Cavalry at the time of the film's period in history.
Wrong Guidon/Flag. Early on Capt. York (John Wayne) is relieved of temporary command of Ft. Apache by Lt. Col. Thursday (Henry Fonda) whom then orders him to return to HIS Troop which we learn is "A" Troop. A bit further on in the movie York (Wayne) is ordered to take a platoon from "A" Troop and trail the telegraph repair crew at a striking distance. A moment after that we see that strike force headed by Capt. York being lead by a Trooper/Standard Bearer carrying a "C" Troop guidon/unit flag.
When Col. Thursday leads a company "at a striking distance" from a repair patrol lead by Lt. O'Rourke. Sgt. Mulcahey is part of O'Rourke's patrol, but when the action shifts to show Col. Thursday's company in a saber charge against the Apache's there is a clear shot of Sgt. Mulcahey riding next to the flag bearer with his saber drawn. Note: this scene was duplicated from Col. Thursday's final charge against Cochise.
During the Grand March at the dance, the actors perform the first round (couples) leading with the dance-favored right foot. When they double up to 4s and then 8s, they are leading with the military-favored left foot.
As the regiment is heading out, we see Philadelphia standing to the far left of Mrs. Collingwood and Mrs. O'Rourke. Soon after, she is on the far right, which indicates she moved. However, right after the close-up of her standing on the far right, the next immediate long-shot has her standing on the far left again.
As York and Thursday are about to leave to trail Lt O'Rourke and the repair wagon, Thursday tells York that he doesn't like exposed galluses. Galluses are suspenders. After that, in every scene almost everyone - including officers - are wearing exposed galluses.
During the dance in the Sergeants Mess, when the dancers are coming round in front of the camera in fours, one of the dancers curtsies, but none of the other women do this. They had already done so in a previous shot and obviously the woman must have been confused.
As York and Thursday are about to leave to trail Lt O'Rourke and the repair wagon, Thursday is wearing a blue kepi with a white cloth in the back to protect his head. When they arrive at Meachem's, he's still wearing the kepi with the cloth. However, as they charge after the Apaches chasing the repair wagon, where's Thursday? There is nobody wearing a kepi in the whole charge.
When Lt. Michael O'Rourke and Philadelphia goes riding, they stop for while with a high and peaked boulder on their left-hand side. In the next shot, when they renew to ride, seen away from the other side, the boulder has changed to a large and low one.
When Philadelphia seeks aid with getting her quarters in order, the call went out for Mrs O'Rourke, when she arrives she runs through the door followed by another woman. When the camera angle changes from the exterior to the interior only Mrs. O'Rourke is inside.
When Capt Yorke reports to Col Thursday at the NCO's dance, he says that Cochise and his people have crossed the Rio Bravo back to American soil. This movie takes place in Arizona, there is no river separating Arizona from Mexico. The Rio Bravo (Rio Grande in US) separates only Texas and no other states from Mexico.
The canyon that Captain York and Sergeant Beaufort ride into to meet with Cochise is supposed to be in Mexico. It is the same canyon that Col. Thursday and his command ride to defeat in the United States.
When Cpt Yorke, with Stg Beaufort, first sets out to see Cochise he simply heads off on his horse, taking no water or supplies (there are no packs on the two horses). This journey must be at least day each way as the whole of the US Cavalry has failed to find Cochise.
As York and Thursday are about to leave to trail Lt O'Rourke and the repair wagon, Thursday tells York that neither he nor his men have their hats worn correctly. They should be worn creased fore and aft like a fedora. After that, in every scene almost nobody has their hats creased like a fedora.
Thursday's final attack was militarily foolish: an outnumbered blind charge into an hidden enemy position. Okay, Thursday is vainglorious and has no respect for the Indians, so he does it anyway. However, once inside this trap in the canyon with Apaches all around, instead of his troops riding out of the canyon they ride about half way out, then all jump off their horses to take minimal cover in a depression with enemies still surrounding them. Their horses continue to ride out, so there's no reason the troopers could have continue. Thursday was knocked off his horse and isn't part of this decision, so his vainglory can't be the reason. It made no sense militarily or otherwise, and resulted in their slaughter. The charge was dumb, but not retreating fully simply made no sense at all.