At the beginning of the chase scene, Johanna is sitting in the wagon on Captain Kidd's left side. She switches to his right side then back to his left side before the wagon comes to a stop.
After Captain Kidd gives John a newspaper, he's clearly seen holding it in his hands; as they ride off John's right hand is free and he rubs his nose with his left, and he doesn't have a newspaper.
Wichita Falls did not gain it's name until 1876.
During the shootout in the hills, Captain Kidd fires at least12 shots from a Remington New Army revolver before he's shown reloading it. The revolver holds only 6 cartridges.
Johanna Leonberger was taken to her Aunt & Uncle Leonberger. But then her aunt revealed that Johanna's mother was her sister. This might make it seem unlikely that Johanna & her aunt would have the same last name unless her aunt and mother had married a pair of brothers (which often happened), in which case their last names would be identical.
Obvious stunt double when Captain Kidd is galloping at the end of the movie (1:46').
At 1:12'46: Fred Hechinger breaks the fourth wall very briefly by looking at the camera before casting his eyes further to his left.
Although the Clifton Record is a real newspaper in Clifton, Texas, it did not begin publication until 1895 and was not in existence at the time the movie is set.
When Johanna loaded dimes in the shotgun shell, they were a of a much more recent design than the 1870s version.
At 16:00, when Kidd is reading the news, he says "...that will have a bearing on all these travel issues." The use of "issue" to mean "problem" would not become vogue until the 1980s (over 100 years in the future of the setting of the story).
John Calley calls the Central Texas area "Kiowa country" when he splits from Kidd and Johanna. However, in 1870 that area was unquestionably Comanche territory ("Comanchería"). The Kiowa roamed further north.
There are no mountains of the kind seen in the film anywhere between Dallas and Castroville, nor is the area just south of Dallas (as seen in the shootout with Almay) dusty and rocky; it is actually quite green and fertile. The film was shot near Santa Fe, New Mexico, which has topography that differs significantly from North and Central Texas.
Early in the film, Captain Kidd and Johanna leave Wichita Falls for Dallas. Based on the position of the Red River, the pair are traveling west. However, Dallas is east of Wichita Falls.
The Red River flows West to East, meaning someone standing on the Texas side looking north across the river would see the river flowing from left to right however in the film the river is flowing right to left, indicating that they must be standing in Oklahoma and staring across at Texas. This cannot be the case since the ferry sunk plus there were Indians on the opposite side.
Mrs. Boudlin states that Johanna is soaked but she does not take the time to strip her of her clothes before putting her on the bed and laying a single cover on her.
When Kidd arrives in San Antonio, he goes to the office of his friend and lawyer. The lawyer introduces Kidd to a colleague as "Jeffrey Kidd". Kidd's name is Jefferson.