New VW Beetles are in the streets of Paris in 1997, even though the car was not widely available in France until the summer of 1998. The filmmakers knew this - Jean-Pierre Jeunet thought the car reflected the "sweet and amusing personality of Amélie".
When Amélie talks to Georgette about Joseph, she says, "He always sits here, right?"(Il s'assied toujours là, d'accord?) Georgette responds "Ben, oui." (Basically, "um, yeah.") The English subtitle "at number 8" (huit) is incorrect.
On the flyer advertising the loss of his album, Nino states he lost it near Gare du Nord. Although this station and Gare de l'Est are very close to each other, Nino lost the album rather next to Gare de l'Est.
After Nino witnesses Amélie putting his album back into his scooter at the park with the Monmarte carousel he runs down some stairs and bumps into a couple. The scene cuts to Nino running down a different set of stairs with no couple behind him. Immediately after there is another shot of Nino running down stairs with the same surprised couple he ran into moments earlier behind him.
The first time Amélie goes to cause mischief in the grocer's apartment, there is a shot of her hand unlocking the door. The sleeve of her shirt in that shot is different from that of the shirt she is wearing inside.
When Nino pursuits the man in the red shoes they both turn to the right side of the station, leaving trains to their left side. In the next scene (shot from outside), they come out of the left side exit, with the trains on their right side.
When Amelie is in the bathroom and she watches the news on Princess Diana's death, she has a perfume bottle in her hand, she throws the lid of the bottle (she is IN the bathroom), after the lids crashes into the wall in the next shot Amelie is OUT of the bathroom, she looks the floor searching for the lid and gets back into the bathroom.
At the end of the film when she's imagining Nino going out to Collignon's for yeast, and rustling the hanging beads at her kitchen door, the cat shouldn't be in the apartment to do that. The stewardess returned with the gnome from her latest trip at least a day earlier, and she would have picked the cat up then.