Revealing mistake: After the explosion blows a hole in the wall and Tuco joins the procession of people flowing down the street, when the shot switches to face the characters you can see that the 'woman' in a blue dress in the wagon is actually a man. (Time is for the extended version of the film).
Factual error: When Angel Eyes arrives at the Confederate Army Hospital, the Confederate flag that is flying is not the correct flag; it is the flag that people in the 20th century and later think of as the Confederate flag. The only rectangular flag with the blue St Andrew's cross on red was the Confederate navy flag and the battle flag of the Army of Tennessee, which was the standardized battle flag for the Western Armies (but not that far west) after January 1864, so didn't exist in the New Mexico campaign, nor at the time the story takes place.
Other mistake: Director Sergio Leone uses one of his trademark filming techniques throughout this film, where anything outside the camera frame doesn't exist. Several times the characters react to situations and other characters when they come into frame that they logically would've seen much sooner. For example, at one point Blondie and Tuco are walking and stumble across an army camp. Even though in reality they would have been walking toward it for a long time and would have been aware of it, they react with surprise the moment it appears on screen.
Factual error: Extended version. After finding a dying Bill Carson, Tuco arrives at an outpost looking for a hospital. It's night, or at least dark outside - he is told the hospital is 18 miles away. In the next scene he arrives at the hospital at nearly high noon. A horse canters and gallops (full speed) between 4-30 mph. Basically the hospital was an hour away.
Revealing mistake: When Blondie is to be hanged by Tuco, and saved by an extremely lucky hit by a Union mortar, you can see that the wall that will be hit by the grenade has been blown to pieces at least once before; the bricks have no mortar between them, and there is a large circular scorched area on the brick wall.
Continuity mistake: Towards the beginning of the movie, Angel Eyes rides up to a house where he has to get information from a man inside and then kill him. After Angel Eyes kills him at the kitchen table, his son runs down some steps behind Angel Eyes in the background with a rifle in his hands. Angel Eyes pulls out his revolver, turns around quickly, and shoots him dead. Take note that the pistol is not pointing directly at the boy as he is firing it.
Other mistake: Blondie suffers from severe sun burn wounds in the face, after the capture and dragging through the desert. The wounds look perfectly realistic, but disappear or change several times. The burns are completely gone shortly after leaving the monastery. Such burns would leave scars and traces for at least weeks.
Continuity mistake: When Tuco is riding his horse, he encounters three bounty hunters - one fires a shot making the horse misstep, and fall, bringing Tuco down to the ground. One of the bounty hunters ask Tuco, "Hey amigo, you know that you have a face beautiful enough to be worth $2,000.00?" He has a big blade of grass between his lips as he backs away from Blondie (Eastwood), however, there was no blade of grass between his lips when Blondie and he were close to one another. As he backed away, he had a rifle in his right hand and a wanted poster in his left, and he knew that Blondie had a gun pointed at him through his overcoat, so he was not able to put a blade of grass between his lips at any point.
Factual error: When Tuco is in the gunshop messing around with the guns, one gun has the cylinder and barrel moving back and forth by manipulating the trigger guard-lever. This is a Belgian Galand & Somerville revolver, a gun that did not exist until 1868. This film takes place during the US Civil War, which ended in 1865.
Character mistake: At the confederate prison camp after they are captured a soldier comes up to the sergeant (Van Cleef) and informs him that the "Captain" wants to see him right away. In the next shot with Van Cleef where he is talking to the commanding officer you will see that he is not a captain but a major.