How is Mercutio a round character in Romeo and Juliet?

A character is considered "round" when they display several different personality traits including faults and virtues. Mercutio certainly shows several virtues. He is flamboyant, humorous, loyal and courageous. Unfortunately, these virtues could also be considered faults. 

Mercutio displays his flamboyance and flare for being the life of the party from the moment he is introduced in Act I, Scene 4. His Queen Mab speech is inspired and shows Mercutio's intense ability to improvise. In the Zeffirelli film, the actor does an excellent job at showing that much of the speech is made up on the spot. It includes fantastical details as well as a focus on violence ("And then dreams he of cutting foreign throats") and sexuality ("Making them women of good carriage"). 

He is likewise humorous, especially in Act III, Scene 1 when he is mockingly ironic in his description of Benvolio as a fighter. Benvoio, of course, is harmless and good, as his name suggests. He's also a peacemaker. Nevertheless, Mercutio pictures him as a brigand and instigator. He says, 

Thou—why, thou wilt quarrel with a man that
hath a hair more or a hair less in his beard than
thou hast. Thou wilt quarrel with a man for cracking
nuts, having no other reason but because thou
hast hazel eyes.

Mercutio even jokes and puns to his death. In his final lines before dropping dead from the wound he received from Tybalt he says,

No, ’tis not so deep as a well, nor so wide as
a church door, but ’tis enough. ’Twill serve. Ask for
me tomorrow, and you shall find me a grave man.

Mercutio is loyal and brave. He defends Romeo against Tybalt. He cannot abide Romeo's display of acquiescence in the street. Tybalt wants satisfaction because Romeo crashed Capulet's party. He calls Romeo a villain, but when Romeo backs down for good reason (he has just married Juliet), Mercutio steps in and challenges Tybalt. He cannot stand that his friend has been insulted. He says,

O calm, dishonorable, vile submission!
Alla stoccato carries it away.
Tybalt, you ratcatcher, will you walk?

Mercutio's virtues also manifest themselves as faults. Moreover, those virtues often turn obnoxious and arrogant. His arrogance will not allow him to be anything but the center of attention. Rather than listen to the warnings of both Benvolio and Romeo he foolishly fights Tybalt, despite the edicts against such violence from the Prince who has proclaimed that the death penalty would be punishment for such an offense. Mercutio also reveals himself to be spiteful as he curses the Montagues and the Capulets in his final words. He says, "A plague o’ both your houses!" That Mercutio is quite well developed and indeed "round" cannot be disputed. In the end, he is killed off to expedite the plot, but also because Shakespeare may have felt he was stealing the show and had to be done away with in order to get on with the tragedy of the title characters.