When Fern's brother Avery sits down for pancakes, his plate is empty. In the next shot (when his frog pops out of his jacket for a second) his plate has a stack of pancakes complete with butter and syrup. In the shot after that his plate is empty again and he is reaching for some pancakes.
When arriving at the fair, the lettering on Wilbur's crate has quotation marks around the phrase "Zuckerman's Famous Pig." These quotation marks were not present when the crate was shown earlier and they have disappeared again by the time the crate is in the pen.
When Templeton rips off a flap from a packet of popcorn that was in the dump, there is no writing on the flap. When Templeton brings the flap back to the farm, the word "CRUNCHY" can be seen on the flap.
Shortly after Avery's frog leaps over the pancakes, one of them slips out from under him. When the pancake lands on Wilbur's head, there is butter on it. In the very next shot, however, the butter has changed to syrup.
In the beginning there are ten piglets suckling from John Arable's sow then when the runt appears there are nine. It happens again when John picks up the runt, planning to kill it, until Fern comes outside to rescue it.
In the beginning of the movie when John Arable's sow is nursing a litter of 10 piglets when Wilbur appears there are nine piglets nursing. When the runt tries to feed there are ten piglets. In the next scene there are nine.
In the beginning of the movie when Fern first gets Wilbur, and the montage of scenes takes place, Wilbur's size clearly changes from very small to almost half Fern's size in between shots. When she gets to Henry's house, Wilbur is back to being very small.