Traffic lights are shown during Edgar's drive through Paris with the cats. Apart from a traffic light installed in 1868 (which exploded in 1869) in London outside the Houses of Parliament, traffic lights were first used in 1914 in Cleveland, Ohio, four years after this movie takes place. (with three-color traffic lights first used in Detroit in 1920.)
When Marie hops up onto the piano, the lowest keys are hit, but the sounds come from keys in a much higher register. The same thing happens when Berlioz slides down the keyboard to get back at Marie for pulling him off the bench; the keys sound much higher than they should.
While Marie and Berlioz fight, Toulouse accidentally drops a candle on Marie's head. When Duchess arrives to scold them, the candle can be seen lying next to Marie. A couple of shots later, the candle is gone.
In the first shots of the milk delivery truck driving down the road no crank handle is seen on the front bumper area. However, after O'Malley stops the truck, the driver gets out and restarts the truck with the crank which is now visible.
When Edgar gives the cats their milk, as he is exiting the room saying "Sleep well...", the cuff-link on his right hand (which is usually seen as red) is seen uncoloured (or just white) for a few frames, and then reappears as red again.
During the country dogs chase, Napoleon bites a hole in Edgar's pants, which are intact moments later. He bites them again at the mill, but the pants remain whole throughout the rest of the sequence. Also, Edgar's shoes are removed and lost, but he still has them later.
When Toulose is painting, he steps on the tube of blue paint and we see it squirt out and land on the floor next to Berlioz. Once Toulose has finished the painting, the paint on the floor appears red instead of blue.
The character of Duchesse is very different in the second scene (the will), than in the rest of the film. In particular she has her nose more clearly defined. The rest of the scene seems also to have been designed by different animators, who used a more "sketchy" style.
In the scene where Thomas O'Malley is saving Marie after the train passes, he grabs a log. You can see the white boot marking on his foreleg disappear. When his paws go into the water and come out, the white marking reappears.
Toward the beginning of the movie, when Edgar is trying to get away from the dogs, a windmill is shown attached to a house (or some other building). When Edgar crashes into the windmill, there is no attached building.
When Edgar and the dogs chase each other with the motorcycle, the background shows the windmill with a door in tact, but moments later when Edgar plows through the windmill on the motorcycle there is no door on it.
When Edgar first hears that the cats were the primary inheritors, he begins to plot their demise. He imagines millions of dollars, with "$" signs dancing in his eyes. But since the movie was set in France, the money unit should have been francs.
In the beginning credits, they show that the song She Never Felt Alone by Robert B. Sherman and Richard M. Sherman is in the movie - but the song never played in the film. The first part was supposed to be played before the lawyer came into the bedroom that the will was created at by the old woman, and the second part was supposed to play when Dutches explaining to Thomas why she has to return to Paris.