A Midsummer Night's Dream adheres to the Elizabethan and Shakespearean model for a comedy. Comedy in the Renaissance had taken a different turn from Greek Aristotelian comedy, a point Ben Jonson expresses dissatisfaction with in the Epistle to Volpone. In Renaissance and Shakespearean comedy the convention had come to be that a happy ending was prescriptive, whereas in Greek comedy the ending was to fit the nature of the character's behavior, whether that required a happy or an unhappy ending. A Midsummer Night's Dream also shows another change in the structure of comedy by the introduction of fools and clowns.
Fools are city dwellers who mishandle language on purpose for wit. Clowns are country folk who mishandle language because they know no better. Both fools and clowns give critical information to move the story along and provide the erotic distractions that were originally coupled with comedies of festivals. In A Midsummer Night's Dream, Bottom and his band of "rude mechanicals" fill the role of clowns.
Some other characteristics of the Elizabethan comedy present in Shakespeare's A Midsummer Night Dream are the presence of plurality of characters and plots. Not content with getting one couple joined, Shakespeare gives us two principle couples and several subsidiary couples to be entertained with. The festival background is identifiable in this comedy because of the celebration of fertility that it ends with: The couples don't make their way to church watched over by calmer adults, as in As You Like It, they celebrate their love and fertility in the woods before returning to the city. Which brings up another Shakespearean comedic element relating to city and woods.
In the city, authority rules and propriety dictates behavior. The couples escape to the woods to revolt against heavy-handed authority and to embrace the governance of love and emotion. The objective, which can be seen in A Midsummer Night's Dream and even more clearly in As You Like It, is to strike an equilibrium, a balance, between the freedom the woods stand for and the formality and order the city stands for. Disguise and deception are integral parts of how the structure of the city is overturned and the liberty of the woods is brought forward and, ultimately, into balance with the other.
[For greater detail on Shakespeare's comedies, see Cambridge Press's The Genres of Shakespeare's Plays written by Susan Snyder.]
To me, this play is a fairly typical comedy of William Shakespeare. It has many of the elements that Shakespeare tended to like to put in his comic plays.
This play has an original problem -- that Egeus will not let Hermia marry Lysander even though they are in love -- that causes the rest of the play to happen. This is similar to how Bianca's problem (having to wait for her sister to get married first) sets up the whole play in "Taming of the Shrew."
Like other Shakespearean comedies, this one has many people changing identity. We can see this in other plays such as "12th Night" or "Taming of the Shrew." Finally, the play ends with a wedding and a feast, just as "Taming of the Shrew" does.
These are a few of the elements of this play that make it similar to other of Shakespeare's comedies.