What event in Act 3 caused the most problems for Romeo and Juliet? Why?
I think it was Mercutio's actions that were the primary cause for extra problems in the play Romeo and Juliet by William Shakespeare. Romeo has a secret reason he cannot share with his friends for no longer wanting to hate/duel Tybalt - he is now part of his family, they are kith and kin. All may have been resolved happily if Mercutio had not been the fly in the ointment. He decides to 'pile in' instead, and sort of forces Romeo's hand to act. Romeo no longer wants any trouble between the two families (now united into one through him) but hasn't had time yet to tell Mercutio about it. In the suddenness of 'battle' he steps between them to influence the outcome - and it is 'under your arm' that Mercutio gets wounded, dying from his injuries minutes later. Suddenly, the situation is exacerbated beyond Romeo's worst nightmares and events will have to run their course.
To me, the major event of Act III comes when Romeo kills Tybalt. This is the turning point in the play and it will cause Romeo and Juliet to die.
After Romeo kills Tybalt, the Prince banishes him from the city. Also, since Romeo has just killed Juliet's cousin, he and Juliet can't reveal that they are married.
Because of these things, Juliet has to pretend that she's going to go through with marrying Paris. Then she has to agree to Friar Lawrence's plan to avoid marrying Paris.
Because Romeo is out of the city, Friar Lawrence can't tell him the plan for making it look like Juliet is dead. Since Romeo think she's dead, he kills himself and she kills herself when she sees he's dead.
So Romeo killing Tybalt in Act III causes all these tragic events to occur.
The killing of Tybalt by Romeo in Act III is the turning point of the play. Up until this point there could have been a happy ending, and Romeo and Juliet's belief in their own specialness in being able to rise above the circumstances that doom their love could have been proven accurate. Romeo's acts up until this point, his reaching out in love and friendship to Tybalt (who is having none of it), show he believes that his love for Juliet and the light he feels shining on him will protect him from the violence and hatred he finds in his world. When he kills Tybalt, he realizes he has not escaped doom.