The way Shakespeare's characters speak tells us a whole lot about who they are. As a general rule, the nobility tend to speak in blank verse while the commoners speak in prose. (Check out "Writing Style" is you want more specifics.) What's interesting about the Henry IV plays is that Prince Hal, who spends a fair amount of time hanging out with his low-life crew, easily switches back and forth between prose and verse, which is a sign that he can fit in anywhere and assume just about any kind of character role.
Shakespeare seems to have the most fun with the commoners. The swaggering Pistol loves to use outrageous language and often misquotes the lines of famous Elizabethan plays (like Christopher Marlowe's Tamburlaine II, a play about a mighty war hero.) Pistol's a swaggering fellow and an aggressive brawler who tends to be comedic, just like his language. Mistress Quickly is famous for her malapropisms (the substitution of an incorrect word for a word with a similar sound). When she says Falstaff "is indited to dinner at the Lubber's Head," for example, she means to say he is invited to supper (2.1.7). The verbal blunder makes her seem a bit foolish and it's also kind of funny, especially because Quickly really does want to see Falstaff "indicted" (formally accused of committing a crime) for breaking his promise to marry her and swindling her out of money.
Mouldy, Shadow, Wart, Feeble, Pistol. Shakespeare sure has a lot of fun with names in this play, don't you think? Not only that, but names go a long way in establishing a sense of character in Henry IV Part 2.
Shakespeare doesn't have much leeway when it comes to the names of the historical figures he portrays (there's not much one can do with "Henry") but he more than makes up for it with the names he assigns the commoners. Shadow and Feeble, for example, aptly describe some of the men in the rag-tag crew of men Falstaff considers consigning (drafting) as soldiers. These guys are physically unfit to serve in any army. Pistol is the name of a "swaggering" Eastcheap fellow who uses outrageous language, tries to bully women, and loves to brawl in taverns. Justice Silence, as you may have guessed, is so named because he's not much of a talker (until he gets drunk and starts singing dirty songs).
Shakespeare even mixes it up with Doll Tearsheet and Mistress Quickly, which brings us to the infamous ladies of the Boar's Head Tavern. Mistress Quickly is an unmarried (and newly widowed) tavern hostess associated with sexual pleasure and prostitution – the name "Quickly" recalls the kind of brief sexual encounter one might expect in a brothel or a tavern. Doll Tearsheet, is also an appropriately bawdy name for a prostitute, which is exactly what she is. The word "doll" is Elizabethan slang for a woman who exchanges sex for money and "tearsheet" refers to an unpleasant physical consequence of a rough sexual encounter.
Just in case the audience doesn't get any of this, Falstaff takes every opportunity to come up with witty puns on each character's name.