Continuity mistake: Sabrina arrives at the Larrabees' party with a black, lacy handkerchief in her hand. When she starts dancing cheek-to-cheek with David, the handkerchief hangs down gracefully from their joined hands. The camera briefly cuts to his mother and his supposed-to-be mother-in-law, and when it cuts back to them the handkerchief is stuffed into her glove. (She could have done that in between, but then she would have had to let him go, and the intimate way they are dancing doesn't suggest that at all.)
Continuity mistake: Sabrina's slightly unruly hairdo is a continuity problem throughout the movie. This is especially noticeable in the sequence which starts with her calling Linus in his office from the lobby, and ends with her leaving the office after learning about his plot. When she makes the call her bangs are full and fluffy, but in the office they look rather cemented and change from shot to shot.
Continuity mistake: When Linus goes to the tennis court in place of David to meet Sabrina, he pours champagne for Sabrina and himself and they start to dance, each holding a glass. The next shot the glasses are gone from their hands. At first glance I thought glasses left set completely. Upon further observation noticed they are on the floor under the tennis net.