Very near the end of the song "Stars," a shot from behind Javert shows he is facing Notre Dame and the moon is in the sky to his right. Although the moon is to his right and illuminates buildings in the background from that perspective, the light reflected off of Javert's forehead is coming from his left.
During the final act (1832), Javert wears the medal of a Chevalier of the Legion of Honor. The medal is the modern version, a five-pointed Maltese Cross mounted on a green palm wreath. The period version had a bronze wreath.
When Javert gets the letter from Paris informing him that "Valjean" has been caught, the tricolor French republican flag is seen hanging in the street. But this scene takes place in 1823, during the Bourbon restoration. During this time (1815-30) the tricolor was not in use
The bishop is wearing incorrect liturgical vestments. He is shown wearing a dalmatic which is the vestment for a deacon with a stole worn 'priest-wise' on top. A french bishop of this period would have worn a 'fiddle-back' Latin chasuble with crossed stole underneath.
When a young child hops on the back of a horse drawn wagon, very clear views are given of the caliper disc brakes on the rear axle of the wagon. Brakes like this were not used until 1890 at the earliest.
During Jean Valjean's death scene after Anne Hathaway sang her first lines, she was seen ducking as she makes her way to her next position. This was visible when the camera was focused on Amanda Seyfried and Eddie Redmayne.
When Valjean gets down on one knee to tell Cosette of her mother's fate, he appears to reach up and take his hat off. When the camera goes from Cosette back to Jean, his hat is still sitting on top of his head.
When we first see Enjolras speaking before the crowd during "Look Down", he and Marius are holding pamphlets in their hands. When Enjolras sings his line "Where is the king who runs this show?", he raises his hand above his head and the camera does a quick cut for a close up -- revealing that the pamphlet has vanished from his hands.
The goof items below may give away important plot points.
When Enjolras is killed, we see him standing by the window and raising the red flag in his right hand. As he falls backwards the shot changes and we see him fall and hang out of the window, but the flag is now in his left hand.
When Gavroche is shot and killed at the barricade, his eyes are open. When he is carried away from the barricades, his eyes are already shut. But when he is laid in a row with the other dead students for Javert's inspection, his eyes are open again.
After "A Little Fall of Rain", Enjolras, who is wearing a red jacket, and another character kneel down to pick up the dying Eponine. As the shot changes, it is clear Enjolras is standing up while carrying Eponine. However, in the following shot, the other character has Eponine in his arms and Enjolras is kneeling behind Marius.
When Javert is contemplating suicide, he is on a bridge over the River Seine and is east of the Notre Dame cathedral. As we are shown the flowing river and as he jumps into the river, the river current is shown to flow eastward (away from Notre Dame). The River Seine actually flows to the west as it goes past Notre Dame.