The "candle light" in the dark record office is clearly a spotlight.
During the initial fight between Caine and the Indian leader stunt doubles are clear in the throws.
During his conflict with the Apaches, the same shot of Caine blocking arrows is used several times in quick succession.
Caine finds a record indicating his American father's birth in 1826, yet no place in the desert southwest/California was part of America at that time, and would not become so for another twenty years.
When Caine is searching through the birth records, he pulls out an obviously modern binder, with a machine-made label sticker on the front.