The director of the 1996 film version of Romeo and Juliet worked hard to reproduce an old play and set it to a modern setting with modern characters. Thus, setting and costuming were certainly portrayed inaccurately, but that was his purpose.
In terms of character, Romeo matched the impulsive behavior we see in his character in the play. Many of his lines were omitted. For example, we do not see the entire scene with he and Paris fighting to the death in the Capulets' tomb. Mercutio was portrayed as one who likes to hear himself talk and who teases his friends. His character was portrayed with great color as he has during the play. The Nurse was used as a comic relief in the whole play, but we do miss some of her scene talking about Juliet as a baby during which she brings up funny experiences in the real play like when Juliet stopped breast-feeding. Capulet is portrayed as an angry fellow by the end in both the play and movie.
I think the only characters that are ill-portrayed in the movie are Lady Capulet, Tybalt, and Paris. At the Capulets' feast, Paris is portrayed as desperate and dorky, whereas in the play he is a County, this should be an upper-class citizen with the ability to recognize social appropriateness. Lady Capulet and Tybalt appear to have a sick relationship at the feast which may be the director's way of demonstrated Lady Capulet's sadness about Tybalt later.