Malcolm McDowell's eyes were anesthetized for the torture scenes so that he would film for periods of time without too much discomfort. Nevertheless his corneas got repeatedly scratched by the metal lid locks.
Korova Milk Bar is named after the Russian word for cow. Moloko (written on the wall) means milk. The bar's sculptures were based on the work of sculptor Allen Jones. Stanley Kubrick had the milk dispensers emptied, washed and refilled every hour, as the milk curdled under the studio lights. The chairs in the bar were the reupholstered and recycled chairs from the space station in Kubrick's "2001: A Space Odyssey " (1968).
The doctor standing over Alex as he is being forced to watch violent films was a real doctor, ensuring that Malcolm McDowell's eyes didn't dry up.
The snake, Basil, was introduced into the film by Stanley Kubrick when he found out Malcolm McDowell had a fear of reptiles. The stated purpose was to make McDowell's character seem more intimidating, but secondarily it functioned as a practical joke by Kubrick.
Stanley Kubrick: [eyes] Alex's cuff links are bloody eyeballs, and his own eyes are emphasized throughout his "cure."