Witty (and Sometimes Acerbic)
Shaw's dialogue is incredibly witty and smart. For some good examples, you need look no further than some of the exchanges between Undershaft and Dolly, in which they spar about morality and their own personal philosophies.
Dolly's speech upon joining his future father-in-law on the "dark side" shows off this playful philosophizing:
As a teacher of Greek I gave the intellectual man weapons against the common man. I now want to give the common man weapons against the intellectual man. I love the common people. I want to arm them against the lawyers, the doctors, the priests, the literary men, the professors, the artists, and the politicians, who, once in authority, are more disastrous and tyrannical than all the fools, rascals, and impostors. I want a power simple enough for common men to use, yet strong enough to force the intellectual oligarchy to use its genius for the general good or else perish. (408-409)
Sure, Dolly's discussions of his political views are certainly earnest, but he's also displaying some serious philosophical acrobatics as he describes the turnabout in his views. The play as a whole is pretty interested in showing how the characters (and perhaps the audience) could stand to flip their worldview around, and this speech encapsulates the kind of reversals and challenges it's pushing.