While Wayne is holding the baby at the wagon, Pete is asked if he got any information about looking after the baby from its dying mother. He is supposed to say "Do you think I was going to drive the lady crazy?" what he says is "Do you think I was going to drive the lazy crazy?"
Shortly after the three riders enter the desert Hightower discovers that Pedro's water bag is empty and throws it away. As they ride away in a long shot, the water bag is still visible on Pedro's horse.
When the three Godfathers leave the covered wagon with little Robert William Pedro, the canvas is coming loose in the wind. Later when Purly Sweet and his posse arrive at the covered wagon, the canvas is tied down firmly.
The coach car on the train in Welcome has 7 windows, no roof-walk, and the number under the windows. The car at Mojave Tanks, which is supposed to be the same, has 5 windows, a roof-walk, and the number in front of the windows. The 5-window car also has no interior, as seen through the rear door.
When the train stops in town the tender is correct. When it is shown running in the desert the tender is incorrect. It is an oil tender and is incorrect for that time period. The fuel would have been wood.
When Bob Hightower is greasing the baby, Bill Kearny holds up his hat to give shade over the baby. At that point, the sun is high in the east. But in the next shot, when they are finished greasing the baby and are applying a makeshift diaper, the shadow from the covered wagon shows that the sun is to the west.
When Ben Johnston is standing in the buckboard when the sheriff and 3 deputies use it to chase the 3 bank robbers out of town, he has one leg behind him bracing himself to stay standing while the horses gallop. There is a strap secured to the tray of the buckboard and he has the toe of his boot wedged in it to help keep his balance.