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.
Continuity mistake: When Frank first pours the wine for Alex he fills it all the way to the top. The shot changes and he is still pouring the wine however the level of the glass has dropped to half full and he fills it up again.
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