Revealing mistake: During the driving scene, the background is illuminated by non-existent headlights. It's running backward on the projection screen.
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.
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