Mendacity
Brick claims he drinks to escape mendacity and lies, but there is no escape from falsehood in the Pollitt family. Brick is lying to himself about the nature of his relationship with Skipper and his culpability in Skipper's self-destruction and death. Maggie lies to the family about the quality of her relationship with Brick, and everyone lies to Big Daddy about his health. These lies permeate the characters, so that we see clearly how a lie forces a person to split into two or three different individuals, depending who is present.
Unrequited love
The Pollitt men have a tendency to inspire love that cannot be required, including love that dare not speak its name. Maggie and Big Mama both love their husbands passionately and fruitlessly, as they are incapable of returning their affections. Skipper's love for Brick was unrequited as well, by necessity, as Brick was incapable of allowing himself to consider the possibility of a romantic attachment to his friend. Even between the Pollitt men, Big Daddy loves Brick but Brick is too soggy with liquor to reciprocate.
Rivalry
There are several intense rivalries in the Pollitt family, as individuals and couples clamor for the attention and love of the aloof Pollitt men. Gooper and Brick's sibling rivalry is largely one-sided, as Brick has no need to engage in the fight - Gooper lost the contest for his parents' affection the day Brick was born. Instead, the brothers view for a place in their father's will, if not his heart. This rivalry is then foisted on to their wives, who compete mercilessly to see who is the better and worthier daughter-in-law.
Poison
Both Big Daddy's cancer and Brick's alcoholism are characterized not merely as illnesses, but as poisons - something that spreads and contaminates from the inside. The cancer eats away at Big Daddy's body while the alcohol eats away at Brick's soul. The poison theme is addressed explicitly but less literally by Maggie, when she speaks of "venomous thoughts and words in hearts and minds" as the poison devouring the entire Pollitt family.
Proxies
An emotional proxy is an important tool for a playwright - a correlative object allows an emotion or struggle to be represented visually and theatrically. Williams takes this a step further in Cat on a Hot Tin Roof by making his characters conscious of their proxies - in particular, Maggie and Skipper each sleeps with the other as a proxy for Brick. Brick, meanwhile, adopts liquor as a proxy for feeling and remembering, and Maggie transparently uses the excuse of a "ticking biological clock" to justify her need for financial security and sexual gratification.
Difficulty of communication
Big Daddy complains frequently about how difficult it is to speak plainly about hard subjects. He is not alone in this frustration - Maggie also struggles to get through to her noncommunicative husband, who is desperately trying to repress the memory of the friend whose communication attempt he rejected. The click in Brick's head when he has drunk enough symbolizes his peace of mind - that is, the moment that he is able to fully detach from the world, and at which communication with him becomes truly impossible.
Blackmail
A popular manipulation technique in the Pollitt family is blackmail and emotional ransom. In particular, everyone tries to control Brick through holding ransom the two things he most requires in order to function - his crutch, and his liquor. Big Daddy knocks Brick to the ground and holds his crutch ransom until he admits why he drinks. Maggie flushes Brick's liquor down the toilet, and won't provide more until he consents to sleep with her. And the control of the Pollitt estate is also effectively held random until Maggie can produce an heir.
