Continuity mistake: When Tybalt and Romeo fight (just after Mercutio's death) watch Romeo's shirt closely. It is at first dirty and covered in blood then when Romeo is looking up to the sky after shooting Tybalt the shirt looks cleaner with only a few blood stains on it. Also watch the wounds on Romeo's face, the amount of blood on them changes too.
Continuity mistake: At the end of the film Juliet/Claire Danes lifts the revolver to her left temple, in her left hand. After firing the shot and landing, her arm has already fallen before she has.....she lands in an odd position assuming the angle the gun was pointed at, and the original position of her arm.