Known as "cancers" in nadsat, cigarettes are what the characters puff on when they need to appear cool or nonchalant (in the case of the "modern youth"), when they are being philosophical or anxious (in the case of the prison chaplain and Rex, the cop driving Dim and Billyboy's getaway squad car), or just delinquent (the ten-year-old girls Alex rapes, all the kids at the bars, as well as Alex's entourage). What is interesting is how Burgess calls them "cancers," obviously to incite the negative connotation.
The sign hanging on the gate of the country cottage where F. Alexander and wife reside also has real significance. In part one, Alex and co. stumble upon the cottage seeking a violent, fun time. Their actions directly threaten all positive connections of a "home." In part three, as Alex stumbles upon the same country cottage after he being left out to die by Dim and Billyboy, "home" comes to symbolize a place of refuge, solace, and a meeting of minds (between Alex and F. Alexander) against the Government.
Breasts or "Groodies"
In nadsat, breasts are called "groodies." All the girls and women (other than the ten-year-olds) have them. They seem to make the boys wild with desire. Well, at least this is true for Alex, since he's the only source we have, and he does talk incessantly about them hanging out of every woman's shirt, and their pink nipples waving hello at him, he is thereby caused to have the urge to do the old in-out-in-out. So, they very obviously symbolize femininity and sexuality; and, in Alex's case, a rape-to-come.
Everyone at the Korova Milkbar drinks milk. Alex drinks milk with almost every meal. Yet, none of the adults seem to be drinking it. Hmm… Could this mean that the milk-drinking teenagers are bunch of babies? You bet. Here associated with the naïve and immature, milk is the substance for infants – unsophisticated and helpless. For the "modern youth" that nurse on the stuff laced with hallucinogens, the explanation is that they are young people who have chosen to add poison to their otherwise innocent slates, making them the evil youth that they are.
Vellocet, Synthemesc, Drencrom
From the text, we infer that these are hallucinogens added to the milk – a popular drink for the modern youth. Symbolizing evil, these are the poisons the kids choose to be exposed to. While under the influence of these poisons, the youth act out violently and brutally as urchins.
Alex revels in his descriptions of the red, hot blood that oozes or gushes or pours out from his victims. To him, blood is beauty; he experiences aesthetic joy from the blood he sheds. Considering Alex's violent tendencies, and insofar as Alex delights in destruction, blood also comes to symbolize vitality and energy.
Night and Darkness
Alex identifies with the night and all things associated with it. According to him, so do the other "modern youth," since they rule the streets at night. Night and darkness represent a sort of security and privacy that Alex and other modern youth crave. Perhaps because they can't be seen or found as easily; perhaps because it heightens the feeling of anonymity. Either way, as a setting, it certainly enables crime.
Day and Lightness
Alex contrasts night and darkness with day and lightness. Day and lightness are for the "starry folks." Patrol cars are more abundant on the streets and security is ensured. There is nowhere to hide where sun and light are present, as in the case of the holding cell and interrogation room. Alex feels extremely exposed and vulnerable in the day and in lightness. These are not his elements.
Ludvig van Beethoven, Wolfgang Amadeus Mozart, Handel
The Classical composers represent all that is ideal to and sacred for Alex, as these composers have created the highest and purest form of art, and therefore joy, for Alex. The fact that one or more of their compositions almost always accompanies Alex's perpetrating a certain crime – which he often commits for sheer aesthetics or sensory bliss – also bodes well for our interpretation.
The broken elevator in Alex's parents' Flatblock represents societal and moral demise. Indeed, it symbolizes everything that is wrong with the society that Alex lives in. The predictability of its lack of functionality suggests that the societal decay is nothing new and that it's here to stay for a long while.