This is an example of the foolery found in Shakespearean plays. The humor of the first 61 lines of Act III, scene iii is based upon the principle of the Shakespearean Clown, while the seriousness is aimed at making farce of religious and policing systems in England.
Note that the Shakespearean Clown and Fool are two distinct versions of characters contributing to rough Shakespearean humor. The Fool is an urban (i.e. city) person who intentionally manipulates excellent command of English to be amusing. These manipulations make significant remarks on philosophy, politics, virtue and vice, or about individual persons. Contrastingly, the Clown is a country person who is not an adept at language and accidentally turns words and concepts upside down resulting in (1) a funny exchange of nonsense between characters and (2) unintentional wise remarks on philosophy, politics, virtue and vice and about individual persons.
Both Fool and Clown accomplish the same end, but the former (Fool) does so intentionally out of education and experience while the latter (Clown) does so unintentionally out of ignorance and mistaken notions. This applies to Verges and Dogberry, whose relationship is a professional one and a friendship, in that both are country Clowns: they unintentionally make amusing remarks based on wrong words that accidentally comment accurately and with farce (i.e., farcically) upon larger, serious issues.
Are you good men and true?
Yea, or else it were pity but they should suffer
salvation, body and soul.
Nay, that were a punishment too good for them
In this prose quotation from III.iii, it takes a bit of doing to understand, but what Dogberry and Verges mean to say is that, yes, the men chosen for the watch (the city patrol) are good men and true, because if they weren't, they couldn't partake in Christian salvation, and, Verges believes, they will partake in salvation. In contrast, they literally say that it would be too bad (a pity) if they should partake in salvation because salvation is a punishment. To sort this out in respect of what was established earlier about the role of the Clown/Fool, Shakespeare is eliciting humor since the Elizabethan audiences knew full well the ideas of salvation and punishment and knew full well the current debates about religious issues that erupted after the Protestant Reformation. Therefore, the element of farce in this exchange address the serious issue of religious integrity and Christian belief.
The same principles are at work in the dialogue about who should be constable and what the duties of the watchmen are, only, this time, the serious issue being farcically brought to light is policemanship in country seats:
First, who think you the most desertless man to be constable?
"Desertless" means without merit. What Dogberry is literally asking is who deserves least (not at all) to be constable. What he actually means is who is most deserving, most worthy. This pokes fun at and makes a farce of country policing practices, suggesting the worst are in fact in charge. A similar example is the various instructions the watchmen are given, in which various improbable rationalizations (i.e., excuses) are given for doing nothing when challenged in their duties, suggesting country policing is utterly incompetent:
Why, then, let them alone till they are sober ... you may
say they are not the men you took them for.