When Hassan first points the slingshot at the three big guys to save Amir it is crossed but in the next shot it appears to be normal again.
Rahim looks at the picture of Soraya, Amir's wife, and puts it down on the table (at around 20 mins), but we don't actually see where he puts it. In the next shot, the picture is not seen anymore.
In the scene at the stadium just before the Taliban official gives his speech there is a soccer game going on and most of the players are wearing shorts. The Taliban did not allow shorts or revealing clothes of any kind to be worn, even at an athletic event. They imprisoned and persecuted members of visiting Pakistani teams for wearing shorts.
The stoning of adulterers in the stadium is incorrectly depicted. The correct process involves digging two holes. The woman is placed in the hole up to her shoulders with only her neck and head showing out, and the man is placed in his hole up to his knees with the rest of his body showing out.
In the film, when Amir's father is buried, a wood coffin is used. Muslim burial rituals do not permit that. Rather, cloth coffin is used to wrap the dead, then he/she is deposited in the grave on the body's right side with face revealed and directed to Makkah.
At the football stadium scene, women are shown in the crowd watching the football. Not only would a mixed gendered crowd such as that be banned (genders would be segregated), but, the Taliban prohibited women from attending football matches at all.
The last scene shows the kites flying in a strong wind, but there is none at ground level (note her hair), nor matching chop on the water, and the glimpse of a sailboat suggests a breeze from the another direction.
During a 1988 scene in San Francisco, modern-day gas pumps are clearly visible.
(at around 22 mins) When people from the Middle East speak English, they frequently use the word "too" where native American speakers interpret the use of "too" as meaning "excessively" and would instead use "very". Where the subtitles translate what Baba tells Rahim Kahn as "You come here too often" he certainly means "You come here very often" and would not insult Rahim Kahn by meaning "You come here excessively often."