A static character is one who does not fundamentally change throughout a text, and a dynamic character is one who does. A round character is one who is complex, perhaps even contradictory, and would take pages to explain, and a flat character is one who is relatively easy to describe, perhaps only taking a few sentences. On one hand, Beatrice and Benedick could be viewed as dynamic because their feelings toward one another change, but, on the other hand, I'm not sure their characters really do undergo significant development. They must be tricked into loving one another, and their pride must be engaged in order for each one to admit their feelings for the other. Ultimately, their pride continues to define them both until the play's end. That being said, I would classify both as round characters; they may be ultimately static, but they are still complicated.

Don Pedro and Claudio, however, become significantly less proud as a result of their being tricked into thinking that Hero has been unfaithful to Claudio and is not virtuous. Neither initially could conceive of possessing such a personal vulnerability or failing, and, by the end, both have been taken down a peg or two and exhibit less arrogance as a result. That being said, I think they are flat characters because they are not particularly complex.

In comedies, most characters are round, stock, static archetypes.  There is the clown, the villain, the overprotective father, the dreamer, etc...

The only dynamic characters in Much Ado About Nothing are Beatrice and Benedick.  They go from hating each other to loving each other, but they have to be tricked to do so.  So, are they really dynamic?  I think so.  Benedick goes from hating women and loving bachelors to defending Hero and Beatrice's honor by challenging Claudio (a bachelor) to a duel to the death.  That's a change.

The other characters are static archetypes, more or less, especially Dogberry, the bumbling constable, and Don John, the archetypal Bastard.  The others (Don Pedro, Leonato, Hero, etc...) change slightly in response to the plot, but not enough to warrant them as dynamic.  Shakespeare wants to the focus of the laughs to be on our main couple for the high comedy (dynamic characters) and on Dogberry for the low comedy (static characters).