Trivia: In the scene where Alex approaches the two girls at the record stand you can see the original score for 2001: A Space Odyssey, also directed by Stanley Kubrick.
Suggested correction: The album shown in the picture is NOT, as is commonly believed, the soundtrack of 2001, but rather a compilation of movie theme music that includes the main theme of 2001. However, the ACTUAL soundtrack of 2001 is still visible in the scene, just a little earlier: When Alex finishes flipping through a magazine and tosses it down on a counter, one of the records in that shot is the 2001 soundtrack.
Continuity mistake: Look at the scene where Alex beats Georgie and Dim and they fall in the river. Alex politely offers his hand to Dim, and in the background you can see Georgie with no hat. Shortly afterwards, he's got his hat on.
Continuity mistake: When Alex is informed that he's being transferred to the Ludovico center, the governor's arms jump from his lap to under his chin, then back to his lap. (01:06:00)