In the final battle, after Duncan knocks Ursa down and says "Don't make me do this!" you get a good view of his sword's hilt. A few seconds later, after Ursa knocks Duncan down the side of the roof we get another view of Duncan's sword's hilt, this time there appears to be white tape wrapped around it. Another few seconds later, Ursa knocks Duncan down the side of the roof a second time. Ursa's sword has obviously fallen out of his hands, like it did when he knocked Duncan down the first time. You can see it sliding down before Duncan. But in the next shot, you can see only Duncan, and Ursa's sword has suddenly disappeared. Next, it's back in Ursa's hands, but he couldn't have retrieved it that fast.
When Duncan and Jenny are talking on the opera house staircase, the same two extras (women wearing black coats) pass between them twice.
Darius says that the Paris catacombs, were used, during the Great Plague, to empty the city's cemeteries. In fact, Paris didn't begin to start emptying its cemeteries into the catacombs until 1786, hundreds of years after the plague had ended.
After Duncan steps out onto the roof of the Opera House there is a cut back to Ursa. The shadow of the [shoulder mounted] camera and cameraman is clearly visible falling across Ursa as he chases Duncan out onto the roof.