In the episode "The Circus Man", when Mr. O'Hara is telling Laura that his secret potion doesn't work, her braids keep moving from in front of her to in back of her.
In the beginning, Charles goes outside to investigate a noise. When he raises his shotgun to shoot, the usual Hollywood racking noise associated with a pump action shotgun is played. However, Charles is holding a break-action shotgun and thus no pump.
The appendectomy performed on Mrs Oleson would not have been possible until at least 1885, the year the first appendectomy was performed. As Laura Ingalls is approximately 10 yrs old here, the action takes place in 1877.
Some of the men have belt loops on their pants. Belt loops weren't invented until 1922.
In HD TV, it is apparent that both the circus man and 8 year old Laura are both wearing the same shade of "tomato sauce" red lipstick. The man has it smeared well below his lip line as well. This is throughout the show, so no "spaghetti-eating" to explain it.