In the beginning of the movie, during the breakfast scene. There is some salt and pepper on the table. In the early shots of that scene the salt and Pepper are farther away from Wallace, but when he pushes the pepper it is closer to him.
After Wallace and Gromit capture the rabbit in the beginning, a banner for the vegetable competition shows that there are four days left. The next night, after Wallace tries to brainwash the rabbits, the calendar where Gromit has marked the days until the competition shows that there are five days left, before Gromit crosses off one more day, making it four.
During the town meeting scene. Lady Tottington is in front of the bible with angel wings and a light above her. But in the shot after it cuts to victor, the light is now not above the bible with wings.
In the part where you see the lady locking her greenhouse full of carrots there are five locks right in a row on the greenhouse. In the first shot she locks the first three locks. In the second shot she is again locking the third one.
When Wallace and Gromit are trapped by Victor's dead end tree in the road, Victor throws the hatchet into the tree next to Wallace. Wallce, nor his clothes, are touching it. Yet when Wallace tries to run off, we see his suspenders caught in the hatchet. The very next scene, Wallace is next to the tree again, and again his clothes are still not caught under the hatchet.
When the neon carrot sign falls on the hood of the Anti-Pesto van, a big piece of the sign is missing. When the Were-Rabbit bursts through the window of the vegetable shop, the sign now has an even bigger piece missing.
When Gromit presses the button to deploy the lasso, there is a hood ornament on the car, which rotates 90 degrees as the hood opens. But a moment later when the lasso rises (and for the remainder of the chase) the hood ornament is gone. When the car returns to Wallace's house and shakes off the mud, the ornament is back again.
When Victor Quartermaine fires his gun in the church to silence everyone and restore order, you can see a shotgun shell ejected from his gun, but later when he gets the golden bullets to kill the were-rabbit, the bullets are large caliber rifle cartridges.
When Wallice and Gromit are at Lady Tottington's house getting the rabbits, the lever has suck at the bottom, and blow at the top, but later when Wallace is trying his invention, when the camera is facing upward, blow is at the bottom, but later it changes back to the original way it was.
Just before the title of the film appears we see the full moon above the rooftops. The moon is on the left of the scene, but the shadows of the chimney stacks are also to the left. They should be to the right.
The prices in the fairground scene at the Giant Vegetable Contest are in the old pounds, shillings and pence, showing that this film is set before this form of currency was abolished on 15 February 1971 (indeed, Gromit's calendar in one scene shows that 1 September is a Thursday, so the latest this film could be set is 1966). Yet Pesto's technology uses LEDs, which didn't become available until the mid-70s, and diode lasers, which weren't available to the general public until about 2000. However, Wallace has been shown to be a genius inventor, it's quite possible he invented all of these things himself, long before the items became available to the public.
The goof items below may give away important plot points.
In the woods, where Wallace is first seen becoming the Were-Rabbit, he first has to face Quartermane, who throws an axe at him. The axe lands on one side of Wallace, but in the next close up we see the axe on the other side.
When Victor Quartermaine does the "Bag a Rabbit game" at the fair and he fires three shots in quick succession, he is using a bolt-action rifle. This is not possible as there would be a noticeable pause between each shot caused by working the bolt.