Continuity mistake: When Babe is walking through the house, you will notice that several times his feet switch from muddy to clean as the camera angle changes.
Continuity mistake: There is one section where the camera shows the animals looking into the house through a window, but when it shows it from the outside they are looking in through a door. It's around the part where Babe is in the competition.
Continuity mistake: During the sheepdog trial, when all the crowd are cheering after Babe receives full marks, you get a view from the stand. Farmer Hoggett and Babe are standing in front of a pen. Then there is a close-up of Hoggett and Babe, and the pen has disappeared.
Continuity mistake: In the scene where farmer Hogget is filling out the application form for the sheepdog trials. There is a postal address line on the form. In the next shot it is gone.
Visible crew/equipment: In the scene where Babe stands in the doorway and is about to get the alarm clock, there's a shot that shows the cat in front of the fireplace, and she flicks her tail. However, above her you can see a wire manually moving her tail.
Continuity mistake: Farmer Hoggett is an old fashioned man, and naturally his fences are old fashioned and wooden. However, in the scene where the two sheepdogs are rounding up the sheep, the camera follows one of the dogs for a shot, and you can see the fence in the background is much more modern - it's called New Zealand fencing, I think - where in the shot before it was wood.
Audio problem: On the way back to the house, in the back of the horse cart, Babe and Fly are talking to each other. They never open their mouths while they're talking.
Audio problem: There are a few points throughout the film when the animals talk, but their mouths don't move.