Factual error: When Lucy and Charlotte are discussing the view from their rooms, Charlotte says they were to have South facing rooms with a view of the Arno and instead got North facing rooms without a view. Later when they have Rooms with a View - their view across the Arno faces North! The Duomo is on the north side of the Arno.
Continuity mistake: Right after Lucy buys her pictures, she walks on the plaza and takes off her coat, carrying it on her arm. When she starts fainting, William catches her and starts carrying her. Both of her arms are in clear sight and the coat is nowhere to be seen. The shot changes, and then her coat is again wrapped around her right arm, squished between their bodies.