Notice in the scene where Mary and Laura are looking for jars. After Laura finds a couple, Mary closes up the cupboard doors. But when they show Laura up close, the cupboard door behind her is still opened, because you can see the stuff inside.
In this episode, a Walnut Grove townperson (in this case, Mr. Hanson) holds a grudge against someone else, and that person ends up being the only one able to help when a child falls into a hole. In Season 9's Little Lou, there was a similar plot. Harriet Oleson was prejudice against the title character, who ended up being the only one capable of saving Harriet's daughter from a hole she fell into.
Emotionally unstable after her little daughter has fallen down the mine shaft, Caroline Ingalls does what many mothers in her situation tend to do: she blames someone else (in this case, Miss Beadle). Even considering the gravity of the situation, this was incredibly out of character for Caroline, and she never did such a thing again for the rest of the series.
Right after Carrie falls and Jack runs to see her, you can see the hole that she "fell" through. This hole is way too small for a child Carrie's age to have fallen in, even if she was wedged tightly.
The drama is heightened when Laudy discovers a lump of coal and guesses that the hole is actually an air vent for an abandoned mine. However, there have never been any coal mines in Minnesota and there are no coal deposits in the state.
Carrie: (about her sisters) I want to go with them.
Caroline: Don't you want to go into town with me?
Carrie: No. I wanna catch bugs!
Caroline: (laughs) All right.
Mary: Oh Ma, does she have to come? You have to be really quiet to catch bugs.
Carrie: I'll be quiet. I promise.
Caroline: She wants to go so bad.
Mary: (sighs) All right. If we don't catch any bugs, you'll know why.
John Ireland's Character is credited as "Wendell Loudy"
One of the few episodes that centers on Carrie (though she doesn't appear in many scenes). By the end of the following season (1977-1978), Carrie only appears in a few supporting-role scenes in occassional episodes, mainly those centering on the Ingalls family, thereafter, and will disappear completely following the 1981-1982 season (when she and her family move to Burr Oak, Iowa).