In the episode "Christmas at Plum Creek", Laura's horse Bunny is referred to as being male. However, in the episodes "Bunny", "The Race" and "Journey in the Spring", the same horse is always referred to as being female.
When Mr. Olson grabs the reins he calls Bunny a girl. Before that Nellie calls Bunny a "he."
When the family heads into town, Laura asks to ride Bunny. Then, in town, Mary goes to Mrs. Whipple's house while the family deals with Mr. Oleson. But in the next shot the whole family (including Mary) is in the wagon, headed home, singing Jingle Bells. And Bunny isn't there at all.
The leaves are on all of the trees despite it being Christmas time in Minnesota.
Characters keep calling Laura's racehorse a "pony" when it is clearly a stallion and even appears to be a thoroughbred. Ponies are typically short and small---and usually fawn or brown---and with a pot belly, but this black horse is lean, muscular and very tall.
In the store both stoves shown have flues attached - floor models would be bare. The tall stove used to heat the store has no damper on the flue and would waste wood. It is also a fire hazard being too close to other items.
When Mr Oleson comes to collect the pony, it's snowing, but no smoke is rising from the chimney.
Just after Carrie places the silver star on the Christmas tree, Mary looks right into the camera.
In the exterior shot of the house immediately after Pa brings in the turkey he shot, a rectangular piece of equipment, likely from the artificial snow machine, falls from the top right and lands in the snow in the bottom right pile of snow.