In the beginning of the show, after Valjean sings the line "took the silver, took my flight" there's a brief shot of the soldier/policeman stepping up to the mic. However, in that shot you can see Grantaire standing to the soldier's right, demonstrating that that shot was taken from later in the show, when the soldier is actually about to sing the line "you at the barricade listen to this".
The army uniforms throughout the play are wrong for the period of 1815-1833. They look to be from the original French Revolutionary era, 1789-1799. Many casual viewers of the play, unfamiliar with the greater context of French history, believe that Les Mis takes place during the earlier era, so it may be that the costumer was labouring under this common misconception.
After the 1823 part of the play, the subtitle shows "Paris, ten years later," which would be 1833, but the story depicts the historical events of 1832.
During Young Cosette's solo "Castle on a Cloud", A loud BANG is heard off-camera. The noise has been attributed to the premature popping of one among many balloons secured at the time in nets against the ceiling. They were intended to be dropped into the concert hall along with confetti at the show's finale. To her credit, Hannah Chick managed to stay in character, flinching visibly as any scared little child would, but continuing her solo without missing a beat.