Corrected entry: Near the end of the movie Capt. Brittles states that he's an officer of the U.S. Cavalry for four more hours, what he means is that his term expires at midnight that night, this would make the time 8:00 PM however when he makes this statement it is broad daylight.
Corrected entry: Near the end of the film, John Wayne crosses off days on a calendar prominently labeled "1878." A short time later, when he receives his commission as a scout, he says it is signed by "Ulysses S. Grant, President of the United States." Grant was president from 4 March 1869 to 4 March 1877; in 1878, the president was Rutherford B. Hayes.
Correction: The calendar is prominently marked 1876 and it is established at the beginning of the film that the year is 1876 when the regimental commander reads Captain Brittles a list of those killed at the Battle of the Little Bighorn which occurred in June of 1876.
Correction: The time of the year is late June, during the longest days of the year. Sunset would not occur until after 9:00 PM.