In the plaza scene when the man who was killed in the scuffle falls to the pavement, a cigarette butt with a filter is shown between the bricks. Filters were invented in the 1920s and were not in widespread use until the early 1950s.
The very highlight of the soundtrack is Puccini's beautiful aria "O mio babbino caro", from the opera Gianni Schicci - even though the story is set in the Edwardian era (very early years of 20th century) and the opera in question wasn't premiered until 1918.
In the plaza scene when Lucy faints, her photographs do not fall into the blood, her hat does. The hat rolls to the left into the blood pool. When George retrieves the packet, the hat and the packet have switched places.
In the opening, Lucy and Charlotte complain that their rooms face north, and thus they have no view of the Arno river. They switch to south-facing rooms. But the view out of their new window faces both the Arno and the Duomo, the latter of which is north of the Arno. Thus, the new rooms must face north; it is the only vantage point from which one may view both the Arno and the Duomo.
The goof item below may give away important plot points.
After Lucy breaks her engagement with Cecil, she and her mother have tea with the Misses Allen, the cups appear to be empty. Miss Catherine raises her cup, tilts it towards her mouth, and then immediately makes a comment, without swallowing, so it was clear that she had not taken any tea at all.