In Scene 2 of Romeo and Juliet, what problems does Capulet's servant have?

I assume that you are talking about Act I, Scene 2.  If so, the problem that Capulet's servant has is that Capulet has given him a list to read when he (the servant) does not know how to read at all.

This mistake on the part of Capulet is why Romeo ends up at the ball and meets Juliet.  The servant has been given the list and told to go invite that bunch of people to the ball.  He meets Romeo, who helps him read the list.  When he does that, Romeo finds out about the ball and ends up going because Benvolio persuades him to.