When the locomotive couples with the runaway caboose, the knuckle on its coupler is open. However, the caboose coupler is closed, which would prevent the coupling to occur.
The locomotive's tender is loaded with wood, but the engine is obviously an oil burner- as evidenced by the black smoke coming out of the stack.
Charles Ingalls rode a horse hell for leather for miles, and when he stopped, the horse should have been lathered with sweat but was not.
When the kids tried turning the caboose brake wheel, it had chains on both sides. Then in one later scene the chains were unhooked.
When Pa is galloping his horse, trying to catch up with the train, he is on the other side of a long fence. Then, suddenly, he's on the other side, closer to the train, without having jumped or broken through the fence. Magic.
During a long shot of the train traveling from Mankato, the outline of a modern automobile driving on a road can be seen, halfway up the shot.
At the end after the caboose has been caught, the train is shown going backward, even though everyone on it as well as the caboose itself needs to be farther down the line. The train should be going forward so that everyone can get where they need to be.