When Quasi and the gang are off to the circus, Quasi's shoes are brown. Shortly after the circus magic act is over, they are blue.
During the "Le Jour D'Amour" sequence, we see one participant's dress change color from blue to beige then blue then beige, and it stays that way the rest of the movie.
Right after Esmeralda and Pheobus kiss toward the beginning of the movie, Zephyr says, "Yuck". At this point, his shoes are blue. In the next shot, Quasi replies, "Yeah. Yuck", and Zephyr's shoes are brown.
While working as a metaphor for the movie's "beauty is within" message, La Fidele bell is an impossible object: with the interior covered in gold and jewels, it would be both impractical (nobody would see it, and church decorations are meant to be seen) and useless, since the acoustics would be terrible, not to mention the clanger of the bell would damage the decoration every time it rang.
For a movie set in the 15th century, a chef prepares a soufflé. A soufflé didn't come around until the early 18th century.
Madelaine practices her tight rope trick using an umbrella with a walking stick handle. The movie is set in the XVI century, and the earliest version of these umbrellas didn't appear the mid 1800's.
When Zephyr asks Quasimodo who's name he is gonna scream at the festival he mentions that the festival is to take place tomorrow but it is actually suppose to take place the day after tomorrow.