How responsible is Alex for his actions? The way he describes the urge to rape the two ten-year-old girls he comes across, it's implied he acts on uncontrollable urges, but he also willingly drinks spiked milk that makes him more violent. This is probably intended by the writer, as the book deals with the concept of free choice, specifically the choice to be violent.
Internet film analyst Rob Ager theorizes the Ludovico technique in the film doesn't actually work, and Alex is just an Attention Whore laying it on a bit thick to get out of jail and garner sympathy from society (and the audience) for his "plight" as a tool of the establishment.
There's a reason why being a certain age (usually 18) is a criterion for an antisocial personality disorder diagnosis. As it happens, while teenagers might have the intellectual and physical maturity of adults, they lack the moral and emotional maturity of adults. Alex is simply an extreme case of a teenager lacking these qualities, which he gains through advancing in age and maturity at the end of the novel.
Crowning Moment of Awesome: Meta-example. Before filming the scene in which Julian carries Frank Alexander's wheelchair up the stairs, David Prowse, who played Julian, asked Kubrick, due to the difficulty of the task, to film the scene in as little takes as possible. When Prowse said, "You're not exactly known as 'one-take-Kubrick', are you?", the crew reacted in horror, surprised that Kubrick was talked to like this. Kubrick, however, laughed and promised to do his best. The scene was then filmed in only three takes, an incredibly small amount for Kubrick. Even so, Prowse was near exhaustion from the repeated takes of carrying Frank and his wheelchair down the stairs.
Do Not Do This Cool Thing: The film is a horrific view of a society crippled by teenage hooligans, but it actually inspired similar crimes throughout the UK, first during its initial release (enough that Warner Brothers pulled it from theaters in England) and then after its DVD release.
Harsher in Hindsight: The reports in late 2013 / early 2014 of street thugs engaging in an activity called "The Knock-Out Game", where said thugs gang-up on a random stranger and beat the crap out the them for fun, is something straight out of Alex's alley, as shown with the scene at the beginning of the film where the droogs beat up a tramp.
Hilarious in Hindsight: The name of their car is the Durango 95, although it's not a truck or an SUV. Ford released a Durango throughout the 1980s while Dodge Durango SUVs have been around since the mid 1990s.
Hype Backlash: This film is very much a Love It or Hate It, despite being considered a classic, many people despise it for how it glorifies sex and violence and wants the viewer to sympathize with Alex.
Jerkass Woobie: Some people see Alex as this in the second act and the third act, considering what happens to him. A little too sympathetic a label, but his near-raped in prison, his inability to enjoy anything in life, and the merciless beatings at the hands of his victims-turned-victimizers humanize him.
"Well! Well well well! Well well well well well..."
Misaimed Fandom: Burgess described A Clockwork Orange as "a jeu d'esprit knocked off for money in three weeks, and it became known as the raw material for a film which accused of glorifying sex and violence. The film made it easy for readers of the book to misunderstand what it was about, and the misunderstanding will pursue me till I die."
Alex did quite a few bad things, but as soon as he raped a woman in the Singing in the Rain scene, he was beyond redemption. This is partly why the twenty-first chapter is so controversial- a lot of readers think it's simply not in his character to suddenly reform.
The Minister of the Interior arguably crosses this by signing off on the Ludovico Technique in the first place. While he could be seen as well-intentioned here, he's clearly doing it for self-serving reasons, and it's pointed out that the treatment may very well be turned on anyone who resists the government. He's only concerned about crime in the first place because of overcrowding in prisons, seeing as he plans to imprison political dissidents. He's certainly crossed it by the end, when he covers up the whole incident with Alex's cooperation, essentially making a Deal with the Devil to protect himself.
Narm: The face that the old man makes when he remembers who Alex is; it's supposed to be twisted in rage and horror, but the angle of the shot and the fact that he's convulsing while bent completely forward makes it look a bit silly.
Signature Scene: Either the opening oner, the Ludovico technique scene, or the "Singin' in the Rain" scene.
True Art Is Angsty: When the book was originally brought over to American shores, the last "Happy Ending" chapter was left out, since the publishers didn't think Americans would like it. When Kubrick began writing his screenplay, he was unaware of that chapter's existence; he read it only when he was nearly finished, and he decided to leave it out because he thought it would ruin the film's message. (The chapter was added back into the American version in 1986.)
Unintentionally Unsympathetic: Despite Kubrick's camera tricks (especially fish-eye lenses) and the defenestration of Alex, it's pretty hard for a good portion of the audience to forgive Alex for his rather heinous crimes.