Visible crew/equipment: In the record store scene, the camera can be seen briefly in the reflection on the wall while it tracks Alex.
Continuity mistake: When Alex is seeing the prison governor about being released, the governor's glasses are on a pile of papers on his desk. From various camera angles they are on some files, back on the papers or halfway between.
Continuity mistake: When Alex and his droogs come in on Billy Boy making ready to rape the young girl, the first shot shows the lacing of a shoe or sandal on the girl's left calf, but afterward it jumps to her right.
Continuity mistake: When Alex goes out from the cat woman's house, his pants are white and clean; then Dim crash a bottle onto his face and before falling down Alex's pants are dirty at knees. In the following scene, at the interrogation, his pants are clean again. (00:41:30)
Continuity mistake: In the sped-up sex scene in Alex's bedroom, watch the bedclothes spontaneously rearrange themselves.
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)
Continuity mistake: The water in the marina alternates from being wavy when Alex and his droogs are silently walking towards the camera, to completely still a moment later when George is sent tumbling into it.
Continuity mistake: In the film's opening scenes, Dim has a black mark on his leg which is clearly visible. When he and Alex start fighting, it has disappeared.
Deliberate mistake: In the scene where Alex, after having been released from prison, is standing near Albert Bridge and staring down at the River Thames, the tide line, as measured by the bridge's support column, changes several times.
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.
Revealing mistake: During the driving scene, the background is illuminated by non-existent headlights. It's running backward on the projection screen.
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 eating spaghetti with the writer and the two reporter types at the end, Alex has a napkin on the table. When the shot changes at the end of the scene the napkin is gone.
Continuity mistake: When the governor is talking to Alex about having the procedure done, the governor says "Tomorrow you will go..." and the position of his hands changes quicker than he could have moved them.
Revealing mistake: During Alex's fantasy after he says, "I knew such lovely pictures", they show a bride being hanged. You can see the "bride" has a beard.
Continuity mistake: When Alex is welcomed to jail, he has to remove his clothes, which are put in a box by a guard. The guard's right hand changes positions with the camera angles. Sometimes his hand is lying on the box, sometimes on the box cover beside it.
Continuity mistake: When the cops have Alex in the holding cell and he is bleeding, a cop throws a pile of napkins at him and one of them lands on his leg. In the next shot, the napkin has disappeared.
Continuity mistake: At the beginning when Alex and his boys go to the old theatre you can see Billy Boy, who is preparing to rape a girl, then loses his hat and the very next moment he has it on, as if nothing has happened.
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.
Visible crew/equipment: The shadow of the camera can be seen many times on Alex and Miss Weathers during the fight scene in the clinic.
Chosen answer: Since this is a futuristic police state, it's likely that Mr. Alexander was dealt with the way dissenters are often dealt with in such situations (Execution or lifelong imprisonment.). In the book, he wrote literature protesting the police state. (The phrase "A Clockwork Orange" comes from a pamphlet he wrote.) Alex and his droogs kicked and beat him while they raped his wife. A while later, the doctors told him she'd died of pneumonia, but he thinks the trauma made her give up the will to live.
Captain Defenestrator