Continuity mistake: On the inspector's boat Frank's wrists are handcuffed together with a railing between his arms to secure him in place. There is a very short chain between the cuffs, 4 to 5 inches at most. When he's pulled free by a rope from Elise's boat he starts 'climbing' the rope hand over hand. In one shot his hands are over a foot apart, he's obviously not wearing the handcuffs. When he gets onto Elise's boat his hands are cuffed once again, she shows him how to pick the locks to get the cuffs off.
Factual error: Frank and Elise approaching to Venice by train. Train announcement says "Arrival at train station Santa Lucia in ten minutes". Landscape from the train window is green and hilly. I'm from Venice and no way you find such landscape 10 minutes from Venice Santa Lucia. Most probably you would see a gray Mestre, Venice inland city, or a completely flat and not green land (for at least 30 minutes from/to the train station of Venice).
Factual error: When Frank and Elise arrive in Venice, they sail from the train station to a hotel which is also located on the Grand Canal (from the balcony we see the Rialto Bridge). However just after leaving the station, we see Saint Marc's Square from their boat from the other side of the lagoon. That is very far from the station - and not on the way to that hotel.
Revealing mistake: The scene where Frank is chased across the roof tops is shot indoors. First, the light and shadows are very bright - but in the outdoors scenes it is cloudy, and there are no clear shadows. Second, the shadows show almost horizontal lighting - a position the sun does not have in Venice in late morning.
Continuity mistake: The two policemen on board the train take a picture of Franck, which is submitted to the British inspector via email. The inspector sees it on his computer screen and then prints it out. He then goes to the printer, but doesn't take the printout from the printer, but instead from the filing basket to the right of the printer - no-one's moved it there. The printout of Frank's face is there too quickly. It can't be done in such a short time.