Scholars often point to one of the songs contained in the play, "Sigh no more, ladies," (2.3) for a possible theme or overall meaning to the play. In this song, which, ironically, is sung when Don Pedro, Claudio, and Leonato are all tricking Benedick into believing Beatrice is in love with him, Shakespeare says that "Men were deceivers ever," and that women are best off not taking them too seriously or moaning over their lack of faithfulness.
Shakespeare then develops the characters of Claudio, who listens more to idle gossip about Hero than he does actually trusting or loving her, and Leonato, her father, who is ready to have her die rather than believe her against the accusations of Claudio, Don Pedro, and Don John (Hello?? Villain!?). However, on the opposite end of the spectrum, Shakespeare gives us Benedick, who once he determines that Beatrice loves him and he loves her, he steps into the breach against his friends (the prince and Claudio) and lets them know what he thinks of how they treated Hero, Beatrice's cousin. He turns out to be the most faithful, loyal man in the play.
Is there one meaning of the play? I highly doubt it. I think there are layers of meaning that will never completely be understood because we can't ask Will himself about them. But I think he's making fun of men and their fickleness, but also giving us an example of one man who is better than the rest. And that love is awesome! :)