What are some comic elements in Act One of Shakespeare's The Taming of the Shrew?

Well, there are several to choose from, however for me,
one of the most amusing elements is our first introduction to the "shrew" of the title,
and how she estabilishes her shrew-like status with an excellent berating of Hortensio
and Gremio after they are told that none may wed the meek and mild Bianca until
Katharina be married. Note what Katharina says to Hortensio, for
example:

But
if it were, doubt not her care should be

To comb your
noddle with a three-legged stool,

And paint your face, and
use you like a fool.

This
clearly sets the stage for the amusing antics that will happen as Lucentio is desperate
to find someone who can marry this "demon" and "harpy," as she is described respectively
by other men. Katharina's ability to insult and play the shrew gives us a real laugh as
she berates the various men that surround her and gives us a real sense of anticipation
as we wait and see what Petruchio will do with her.