Factual error: When Eddie and Tommy are trying to enter in the security camera room at the beginning of the film, they use real tools but they couldn't unlock a door by using them this way.
Revealing mistake: In the Vatican, when the security cage falls on the policeman, he stays still for two shots because he has been replaced by a dummy.
Visible crew/equipment: When Tommy and Eddie drive away from the prison at the beginning, the crew is reflected on the car.
Continuity mistake: In the ambulance, somebody shoots at the windshield but the hole disappears during the rest of the scene.
Revealing mistake: At Da Vinci's castle, hit Pause when Eddie steals the crystal. It is actually a little frog statue. The prop was apparently unavailable during the shooting of this scene and they took an object of the same color.
Revealing mistake: When Tony and Eddie jump from the Mayflower's building, the ground on which they fall bounces.
Continuity mistake: At the auction, the night guard who recognizes Eddie from the heist has a gun in his hand. Anna makes him fall and it has disappeared when he hits the ground.
Audio problem: When Hudson is being dragged behind the ambulance and the Mario brothers are shooting at him, the bullet that punches through the plastic bag causes a "glass-breaking" sound.
Factual error: The opening voiceover says that the Duke of Milan commissioned the statue of the horse in 1481. The statue was actually commissioned in 1473 and, due to the size of the statue, Leonardo's planning wasn't complete until 1490. The project was abandoned a few years later.
Factual error: The film takes place in 1981 (the film very specifically states that it takes place "EXACTLY 500 years" after the prologue set in 1481), meaning that the several references to the Nintendo Entertainment System don't make sense, since they weren't released until a few years later, in the mid-80's. ('83 in Japan under the name "Famicom" and 1985 in North America to be exact).
Visible crew/equipment: As Bruce Willis and Andi McDowell improbably make their castle-escape aboard the da Vinci glider, a wide, open-air aerial shot looking down shows the model glider pass right through the shadow of the hovering helicopter that is shooting the footage.
Revealing mistake: When Hudson is researching how to steal Da Vinci's book he comes to a staircase. Along the walls are bookcases - if you look properly you can see these are flat, with the book spines just painted on.
Continuity mistake: When Darwin has Tommy at gunpoint in the limo Tommy puts his hand all the way to the wrist through a strap attached to the car. The shot changes and Tommy is instantly grasping the strap with his hand.
Other mistake: When Leonardo lifts up the bar he has just fashioned, you can hear a couple of people in the background say "Gold" where the others are and correctly saying "Oro" (Since the Italian word for gold is Oro).