Carter II Tha Carter II Lil Wayne

list full of problems, I'll address 'em like P.O. boxes

In this line, Wayne is just saying that he has a lot of problems & he addresses them, like P.O. boxes instead of ignoring them; because P.O. boxes have adresses. Its really simple.
Possibly that this person has a large number of things on his mind
Maybe even saying that when trying to deal with one or some, its like looking into a Post Office but you cant remember your Box number.