When Mr. Thomas McGregor opens the white door of his London apartment at No. 10, instead of British Locks, the outside of the door has an Australian Lockwood brand lock, and on the inside of the door is an Australian Lockwood 355 Double Cylinder Deadlock Deadbolt.
The Sparrows that appear at the start and throughout the film are two separate species, one being a Tree Sparrow (who do not show sexual dimorphism and we can assume are possibly female from the voice) and the other being a female House Sparrow. This is odd having two separate species together and was most likely a factual error with someone thinking that a Tree Sparrow was in fact a male House Sparrow.
While the animals are hiding from McGregor, Peter tells the badger, "Just because you can't see him, doesn't mean he can't see you!"
Only the duck has seen the car pulling up in the driveway. Peter has no reason to know that it's a man who is going to enter the room.
The workers that Thomas McGregor (Domhnall Gleeson) speaks to in the hardware store speak in very bad attempts at English accents, indicating that they were almost certainly Australian supporting actors (most of this film was filmed in Australia). The irony here is that Gleeson himself is an Irish but speaks in an impeccable south east English accent in the film.
When the Rabbits are hiding under the Land Rover at the shop, there is no rear axle housing. The Land Rover is 4WD and would have a rear differential housing. Just before the rabbits are revealed it can be seen that the rear axle housing is present. Yet when the rabbits are seen under the car, the housing disappears. Additionally, the shaft between the wheels should not spin because the axle shaft would normally be covered by the housing in a driven axle. The dead axle seen would only appear in something like a trailer, not a 4WD.
The goof items below may give away important plot points.
When Bea and the rabbits are watching Thomas clean the greenhouse, Bea mentions Old McGregor and says "God rest his soul," at which point Cottontail pulls out a blackberry and squashes it, clearly getting juice all over her paw. In the next shot the blackberry is gone and Cottontail's paw is completely clean.
When Peter and his Benjamin go to the toy store to talk Thomas into coming back to stop Bea from leaving, Thomas runs into a storage room and shuts the door behind him. You can see when it shuts that it has a keypad on it to unlock the "employees only" door. Yet his boss June keeps pounding on the door demanding he unlock it. That would not happen. As the boss, June would surely have the access code to unlock the door as well as a physical key if needed.