Revealing mistake: When Anna (little girl who stutters) is crying after being teased, the "tears" on her cheek are obviously fake. They never run or move. I'm guessing rubber cement.
Factual error: When the older boys are lying around the playground discussing The Election, you can see the bottom of the boy's shoe. It is made of molded rubber and features a "tread" on the bottom. This would not be how shoes were made in that time period.
Continuity mistake: When Edwards is first discovered missing by Grace, the moon is in the background in the center of the screen. After all the time that goes by with Edwards in the casino, Charles looking for him, finds him and goes all the way back to where they were sleeping (figure at least an hour or more), the moon is still in the exact same position in center of screen from the exact same camera angle. In reality, the moon would have been more to the right or disappeared completely by now (depending on the timespan).
Other mistake: When Charles takes a horse to chase after Carrie in the hot air balloon, they use a stunt double. He's not even dressed like Charles. Then a few minutes later, they use the exact same stunt man to jump on the hot air balloon. Just looks silly.
Revealing mistake: When Charles steals a horse to chase down the balloon with Carrie in it, you can see it's a stunt double. Charles is wearing his hat, beige shirt, and his knee-high boots with pants tucked in. The stuntman has a pink shirt, no hat, and long pants with shoes. Maybe even white socks.
Factual error: When the hot air balloon comes down with Carrie in it you can see N410AA printed on it. This is commonly called a tail number on planes and is issued through the FAA, which of course did not exist during the time period of the episode.
Revealing mistake: During the scenes when they are chasing the balloon in the prairie, the tire tracks from the camera car are easily visible.
Factual error: When the man is holding onto the rope from the balloon, you can see modern tire tracks in the field.
The Rivals - S4-E14
Continuity mistake: Laura almost bumps into the boy after they get out of the lake and she looks as if she wants to kiss him. In his point of view, he is standing further away from her. In the next shot she is a few inches away from him.
Deliberate mistake: When Mary gets to the school where she is going to be teaching, all the children are standing outside wearing shoes. However when they come in to the school they are barefoot. I have a feeling this was done to show how poor the community she was teaching in was supposed to be, but it looked like too cold and rainy of a day to let the actors be outside barefoot.
I Remember, I Remember - S4-E16
Continuity mistake: Charles is delayed getting home on his wedding anniversary because a wheel on his wagon broke, he had no jack and he had to make repairs during a heavy rainstorm. Rain is still falling late at night and can be seen through the window when Caroline hears Charles arriving. She runs outside to greet him and suddenly there is no rain.
Factual error: A modern day fire extinguisher is shown on a beam Charles walks next to in the town of Bixby.
As Long As We're Together (2) - S5-E2
Revealing mistake: When Charles Ingalls plays his fiddle at the end of the episode, one can see from the movement of his hands that he is not really playing, but just pretending. (Also visible in every other episode where Charles plays the fiddle, but most obvious in this one.).
Continuity mistake: During the final football game, the sun position changes from one side of the field (before the game starts) to the other side during most of the game then back to the first side for the last play of the game.
There's No Place Like Home (2) - S5-E6
Other mistake: At the very end, Mr. Hanson is seen walking toward the church. Because of his stroke, he's slow and unsteady. We see several close-ups of his feet, showing how he's struggling. Two of those shots are the same footage. It's obvious, because you see that he drags his foot over a small stick in the road and stumbles - and in both shots, it is exactly the same.
There's No Place Like Home (2) - S5-E6
Continuity mistake: At the end, when Lars Hanson hears the church bell ringing, he gets up from his bed and goes to look out the window. When he first gets up, his hair is completely tousled - definite "bed head." The shot changes to show him leaning out the window, and his hair is neatly combed. When the shot returns to the inside of the room, his hair is once again rumpled and untidy.
Visible crew/equipment: When Michael Landon is chasing the boy at the carnival, the shadows of the crew can be seen on the bottom of the frame as he is running.
Character mistake: When Eric is asked to spell repetitious at the spelling bee he spells it R E P I T I T I O U S... Alice Garvey says "correct" but it was incorrectly spelled.
Someone Please Love Me - S5-E22
Continuity mistake: Charles walks down the staircase with a small trunk, suitcase, and a duffel bag. He finishes business from the man he bought the horses. When he walks out onto the porch, Charles is only carrying his duffel bag, and tosses it into his wagon. No other luggage is visible.
Other mistake: After the stagecoach crashes and Mary discovers that neither Marge nor Adam can move, she tells Adam that she's going to leave the canteen for him and Marge. Neither one can move. Neither one is going to get the canteen to the other.
Suggested correction: Wasn't Mary the one in the balloon?
Mary was in the balloon earlier in the episode with the man who runs it but near the end, Carrie wondered off into it and it took off with her inside ALONE.