It is speculated that when Shakespeare set Much Ado About Nothing in Messina, he was actually thinking of Venice, which was one of the most corrupt cities of his time period ("The Artificiality of Messinian Society," eNotes). Venice was extremely wealthy as they had a monopoly over trade in China due to the success of the Venetian explorer, Marco Polo, who opened trade routes between Beijing and Europe. Due to the city's wealth, the city's wealthy families were constantly competing with each other for grander palaces and more power. The city's wealthy also ruled the government. Venice was called a republic, however, the Great Council ruled the city, which consisted of the wealthiest and most influential families of Venice. The Great Council selected all public officials, including the Senate body, who elected the Council of Ten. The Council of Ten where the highest administrators and made decisions for the city in secret ("Venice During the Renaissance"). Hence, since Venice was really a wealthy totalitarian city who passed itself off as a republic, we can see that Venice was extremely corrupt and embodied the theme of appearances vs. reality that dominates Shakespeare's play.
Dogberry actually expresses this theme very well when he lists his attributes, which are his position of power, his wealth, and his beauty, which we see in his lines:
I am a wise fellow; and which is more, an officer; and which is more, a householder, and which is more, as pretty a piece of flesh as any is in Messina, and one that knows the law, go to! and a rich fellow enough, go to! ... and one that hath two gowns and everything handsome about him. (IV.ii.73-78)
In this passage, Dogberry places more importance in owning a house then being an officer; he then follows this with placing his handsome looks as being more important than either the house he owns or his position as a law enforcer. He finally culminates his argument by referring again to his wealth and again to his looks, showing us that what is really important to Dogberry, as well as to the citizens of Messina are wealth and looks, or appearances, rather than reality.
It has also been pointed out that Elizabethans viewing the play would have recognized the corruption of Venice that is being alluded to through the corruption of the citizens of Messina ("The Artificiality of Messinian Society," eNotes). One way in which Messina differs from Venice is that the citizens in the play turn out all right in the end. All characters realize their faults, such as excessive pride and gullibility, and make amends, restoring the innocent, slandered Hero to life. We don't know for sure why Shakespeare chose to set the play in Messina when he may have actually been representing Venice; however, it can be said that Shakespeare did not see that as satisfactory an ending could plausibly take place in Venice, therefore, he chose another wealthy Italian port that had its own share of corruption.