Continuity mistake: In the scene showing the kids on the caboose as Charles tries talking to them from the train, the sun is on one side of the kids; then, a short time later in the same scene, it's on the opposite side of the kids (the caboose never made any turns in this scene).
Factual error: On the hill to the right of the kids as they walk away, there appears to be a telephone tower on the hill.
Journey In The Spring (1) - S3-E6
Revealing mistake: When Charles notices that his dad set the house on fire, and he is at his mom's wooden grave site, the wooden grave marker moves when he gets up to save his Pa from the burning house.
Character mistake: In one scene during a rescue attempt for Carrie, Mr. Loudy says to Charles, "It will be dark soon." However, after an immediate camera angle change, it's revealed to be not just broad daylight but, looking at everyone's shadows, it's mid-day (around noon). There will be many hours of daylight left, so Loudy was way off with this comment.
Quarantine - S3-E13
Visible crew/equipment: Around 9:15 when the family is sitting at the table talking, in the lower right corner the shadow of a camera person appears below Ma's chair. (00:09:14)
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).
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.
Suggested correction: I just watched the episode and the tire tracks look to be the same shape as the tires from the wagons that are moving people around (such as the firefighters). It didn't look really thick like automobile tracks, so those seem proper to appear.
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.
Suggested correction: Charles was riding with the firefighters. It wasn't Charles that took the horse - it was Patrick (Mary's friend) who took it. However, yes, there easily appeared a stunt double who looked much older and heavier than Patrick trying to actually pull the balloon down (who easily could have been mistaken for Charles).
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.
Suggested correction: The stuntman doubled for Patrick (not Charles). Charles was seen the whole time as being in the wagon with the firefighters. Patrick stole the horse and went off on his own to save Carrie.
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.
I'll Be Waving As You Drive Away (1) - S4-E21
Factual error: This episode takes place just after Grace was born (1877). Mary would have been 12 during this time frame, but she is portraying a 15-year-old.
As Long As We're Together (1) - S5-E1
Factual error: The start of season 5 took place in 1881 (the year Mary first went to the blind school). In 1881, Grace (born in 1877) would have been around 4 years old by then, but she is shown as a baby in the series.
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.).
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.