Revealing mistake: When Carrie (played by twins) falls down in the opening sequence, it appears that she gets back up and continues running. In reality, after falling, the other twin gets up and continues. If you look closely enough, you can see that when getting up, Carrie is slightly closer towards the camera than when the first twin fell.
Revealing mistake: In the episode where Baby Rose is sick with smallpox, you can see part of a modern disposable diaper under her cloth diaper when Doc Baker is checking for blisters.