We are not told very much about the physical traits of Shakespeare's characters in Romeo and Juliet, especially Mercutio. We are able to surmise a few physical traits from the text, especially a few for Romeo and Juliet. But for the character Mercutio, we are able to surmise very little.
We know that Mercutio is Romeo's best friend and, therefore, might be around the same age as Romeo. While we are told by both Juliet's father and her Nurse that Juliet is not yet fourteen, meaning that she is thirteen, we are never told Romeo's exact age. We do, however, hear Friar Laurence refer to him as a young man, especially in the lines, "Young men's love then lies / Not truly in their hearts, but in their eyes" (II.iii.68-69). Also, we know that Romeo, Benvolio, and Mercutio are old enough to be out in society, as we see them out roaming the streets of town. Therefore, all three are somewhere in either their late teens or early twenties. If they were any younger, they would still be at home being schooled by their tutors. Hence, one thing we can deduce about Mercutio's physical traits is that he is a young man.
Unlike Romeo, we are never told anything about Mercutio's looks. We know that Romeo is one of the handsomest men in town because we see Nurse describe him as such in the lines,
Though his face be better than any man's, yet his leg excels all men's; and for a hand and a foot, and a body ... they are past compare. (II.v.39-43)
Since Romeo is the best looking man in town, we can surmise that Mercutio is not as handsome as Romeo. Yet, judging by how his friends interact with him, we do know that Mercutio is a very popular, very outgoing person, therefore, his looks probably do not fall too short of Romeo's.
One final thing we can deduce about Mercutio's physical traits is that he is very well-dressed. We know this because we know that he is very wealthy. Mercutio is identified with two noble relations in the story. We know that Mercutio is either a relation or a friend of the Capulet family because, when Romeo reads the invitation list that the Capulet servant shows him, we learn that Mercutio has been invited to the Capulet feast (I.ii.70). We also learn that Mercutio is a relative of Prince Escalus's. We learn this when Romeo proclaims it after Mercutio has been stabbed by Tybalt, as we see in the line,
This gentleman, the Prince's near ally,
My very friend, hath got this mortal hurt
In my behalf. (III.i.109-111)
In this line, the term "ally" can be translated as referring to a person who bears a "mutual relationship" with another, either as a friend or even as a family member (Random House Dictionary). The fact that Mercutio is the Prince's relation is later confirmed in the final scene by the Prince himself who proclaims, "And I, for winking at you, discords too, / Have lost a brace of kinsmen. All are punish'd" (V.iii.305-306). In other words, the prince is declaring that because he turned a blind eye to the feud, he lost several family members, including Mercutio. Therefore, since Mercutio is both a friend of the Capulets and a relation of Prince Escalus's, we know that he is of noble blood and very wealthy. Hence, we know that another physical trait of Mercutio's is that he was probably very expensively dressed.
I don't think we can ever really pinpoint some physical features of Mercutio in Romeo and Juliet. We can guess that Mercutio falls into the same age category as Romeo, so around 13 years old. In the Baz Luhrman movie version Mercutio is portrayed by Harold Perrineau, who is an African American and a drug dealer of sorts. There is no evidence in the actual play that Mercutio is black and is a drug dealer, it was Luhrman's own interpretation.