Deliberate mistake: When the Darlings discover the dead rat, they raise the curtain and cry out loud, but the rat is nowhere to be seen. Given Disney's long time history of refusals to show dead bodies or blood, it's highly possible that this was a deliberate mistake, but really awkward indeed.
Deliberate mistake: Several times during the movie the narrator explains what happens while the book flips its pages. During this, every page is identical to the last one so the animation has simply been copied/reused to save time and money.
Deliberate mistake: In "Do You Hear the People Sing?", Grantaire can be seen hijacking the funeral carriage but when the insurrection starts, he is at the tavern with some girl and Marius acts like he wasn't just there. George Blagden who portrayed Grantaire didn't want to be left out of that great set-piece so he was allowed to participate and the director must have thought no-one would notice him.
Deliberate mistake: When the gangs meet in the toilets to set a date for the brawl, the mirror on the left is the only one opaque, most surely to avoid reflections of the filming crew.
Deliberate mistake: Rocks on the water suddenly appear when the rabbit shows up, which allow for Alice to chase him.
Deliberate mistake: In the ambulance scenes, John Goodman is given oxygen via a nasal tube, probably so he could tell his story. In real life, a mask covering the nose and mouth would be used for maximum effectiveness in such a critical situation.
Deliberate mistake: During the song Adelaide's Lament, Adelaide goes to her medicine cabinet, opens it, and there is a cut to a shot from "inside" the cabinet as she surveys all the medicine she takes to treat her "cold." From the inside, the cabinet is almost twice as wide as it is when it shows her open and later close it from the outside.