Continuity mistake: In the fight with Billy Boy, many droogs lose their hats and have them on again many times during the scene. (00:06:20)
Revealing mistake: During the driving scene, the background is illuminated by non-existent headlights. It's running backward on the projection screen.
Continuity mistake: The main character's name is several times in the film mentioned as 'Alexander DeLarge', but in the newspaper articles detailing his release from prison, they call him 'Alex Burgess'. Burgess is the surname of the author of the book the film is based on, so they might have originally intended to name him so as an homage.
Continuity mistake: When Alex, the writer, and the other two political people are sitting at the table near the end of the movie, not only does the amount of sauce change on the spaghetti, but the amount of spaghetti changes from shot to shot even after Alex has stopped munching on it. This isn't part of the director's ploy.