Continuity mistake: In the rain scene after Guido & his princess are in the rain, the steering wheel becomes detached, and he holds it up, and you see hardware still connected to the steering wheel. When he puts the pillow on top of it for her to use as an umbrella, you don't see the hardware. During this scene, Guido places the pillow directly on top of the steering wheel, and in the following shots, you don't see the actual steering wheel; only the stick.
Continuity mistake: When Guido is caught in the spotlight during the liberation of the camp, he climbs down from his hiding place on the wall and falls to the ground. When the guard prods him to stand up the blanket around his waist hangs down to his feet, but when the camera cuts away and back just before he starts walking, it is several inches shorter. When he play marches for Giosuè it is hiked up even farther.
Other mistake: When Giosuè discovers the German boy in the metal box Guido says that his name is Schwarz (Black). The German subtitles translate the name as Schwanz (Tail or - rather - Dick), and that's how both Guido and Giosuè refer to the boy later. Even if the different naming later was intended the first subtitling was too anticipatory.
Plot hole: When Giosuè acts as a silent German boy and joins the coffee party Guido talks to him in Italian quite loudly while he is eating. The two German children sitting at the same table should have noticed something and, if not give him away, at least be somewhat surprised.
Other mistake: When Guido drops Dora at home after he had "kidnapped" her from the opera the rain has stopped. She mentions his wet hat, he takes it off and puts it back on, and when he bends forward a substantial trickle comes running off the brim. There should be no water left (if any) after he had taken the hat off.