When Roddy first meets Sid, they are on the kitchen counter with lots of food that would have to be refrigerated, like a chocolate cake and sausages. Given the fact that the owners of Roddy have just left for a vacation, it would be inconceivable for them to have left all that food out while they were gone away.
As the movie opens, the little girl pours a whole box of rat food (and its box) into the dish at the front of Roddy's cage. When Roddy slides down to the front of the cage minutes later, neither the food, nor the upturned box is anywhere to be seen.
Rita's belt. In the end sequence after Le Frog removes the master cable from Rita there is no opportunity for her to obtain a new belt, yet after the wave is frozen she is shown standing with Roddy suddenly wearing a black shoelace as a belt.
When Sid first appears, he grabs two hotdogs off the counter and runs to the living room to watch TV. During the commercial for the soccer game, Sid throws a hotdog at the TV, leaving a grease smudge on the glass as it slides down. Later when the soccer game is on, no greasy mark remains. Given Sid's lack of cleanliness, it is unlikely he would have cleaned the TV by the time the game was on.
Just before the Jammy Dodger plunges to its watery grave, Roddy and Rita chew through the twine that is holding the "Duty Free" plastic bag in place. They briefly are seen each holding a length of twine that is tied to one of the bag's handles. In the next shot, they are holding the handles for the bag itself, and the twine is never seen again.
In the scene where Roddy falls onto the drawing at the city. Up above him the shot shows he landed in the middle, away from the trees in the picture. In the next shot where he gets up, his right leg is on the trees. How could he land in the middle then all of a sudden appear in another position?
The doll that Sid throws up in the air changes position several times after he discovers Roddy and Rita. It goes from being at his feet to being near the door to being several inches away from the door when he leaves the room.
When Rita and Roddy are escaping from The Toad at the beginning, Rita jumps down repeatedly and ends on the handle of a hammer. When Roddy jumps/falls down the same path Rita went, the hammer has changed, and he ends on the head of the hammer.
At one point in the movie, Spike is incorrectly shown loosening a screw-on cap on a can of "Mixed Nuts" by turning it clockwise to remove it. When the lid pops off, the threads are clearly the standard, counterclockwise-to-remove direction instead. Similarly, when Spike is screwing the liquid nitrogen hose to the chamber Roddie and Rita are in, he turns it counter-clockwise rather than clockwise.
As well as the aforementioned error with the water level in British toilets not matching that shown in the film (Although it can depend based on the model), a large majority of toilets in the UK don't swirl, either.
Several times during the film, someone gets thrown into the toilet which is shown to be almost full with water. Most British toilets have a far lower water level, however this varies depending on the individual toilet and a higher water level is possible.
During the chase scene with Rita and Roddy vs. the other rats, the view towards the bow of the boat shows hanging signs. The reverse view shows the exact same signs in the exact same positions as if the boat were headed in the opposite direction.