When Wilbur is talking to the geese after he plays in the mud, the amount of mud on his side changes.
When Charlotte has caught and wound up the fly in her web, she leaves it and drops down to talk to Wilbur. When she goes back up to her web, the fly is missing.
When Gussy first introduces herself to Wilbur, she has a light yellow spot on the tip of her beak. In the next shot, Golly has the spot on his beak.
Wilbur, a boar (male pig) is played by sows (female pigs). This is blatantly obvious in some scenes.
The hatching goslings are clearly ducks, not geese. Ducks have bright yellow feathers and a flat orange bill, whereas geese are duller gray with yellow underlayment of yellow feathers and a slightly pointed bill.
When Fern is visiting Wilbur before going to school without him the second time, it is raining hard. The road immediately outside is wet, but is clearly dry at the left side of the screen by the fence.
Betsy mentions that she can't play on three empty stomachs, but actually cows have four stomachs not three.
When seen next to to Charlotte, Templeton and Wilbur, the size of Charlotte's egg sac appears to vary. It is disproportionately large when Wilbur picks it up in his mouth.