What purpose do Dogberry and Verges serve in Much Ado About Nothing?

In general, these characters would have been known as the
clowns, since, in Shakespeare's day, comic actors were called clowns.  Shakespeare wrote
for a company of actors, which means that he always knew in advance which actors would
probably play which parts, so we can assume that he actually wrote parts for certain
actors.

Dogberry and Verges would have been played by two
of his company's clowns, so one major purpose that they served was to amuse the
audience.  This pair have some funny lines, but we can also assume that they created
physical humor to go along with their text, since clowns in Shakespeare's day were well
known for their physical comedy.  This is still true today of many comics, actors like
Jim Carey who rely on physicality to create their
humor.

But these characters also serve a purpose when it
comes to the plot.  They are "law and order" in Messina, and they are the ones that
apprehend Conrad and Borachio, after Claudio and Don Pedro are duped by Don John into
believing that Hero has been unfaithful.  Borachio participated in this scheme, and the
bumbling Dogberry and Verges (with the Watch) apprehend them.  They even try to alert
Leonato before the wedding, but he doesn't take them seriously, so it isn't until Hero
has been shamed and has"died" that the truth comes out.

So,
Dogberry and Verges serve two purposes.  As clowns, they are intended to amuse the
audience, and as characters in the story, they serve a pivotal purpose in the plot of
the play.