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: There are a few points throughout the film when the animals talk, but their mouths don't move.
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.