I'm looking for a phrase that describes a person who always thinks about too many things at once and, therefore, looks(and acts) sloppy. Something like: "he has a swarm of vasps in his head". I can't think of anything similar to compare at the moment and I will be sure to update the question when I remember something.
Well, the person you describe certainly lacks focus, so I guess you could say he is unfocused.
You asked, however, for a metaphor or phrase, so here are a few suggestions:
He's certainly the dizziest person I know!
His thinking is all jumbled up.
Sally is certainly muddleheaded at this point in her job search.
Rudy has turbidity of the brain pan.
Martha suffers from excessive ideation.
"The study of law is something new and unfamiliar to most of you, unlike any other schooling you have ever known before. You teach yourselves the law, but I train your minds. You come in here with a skull full of mush and, if you survive, you leave thinking like a lawyer" (Professor Kingsfield, from the opening narrative of the TV show "The Paper Chase")
They say of George, "If he ever had an original thought, it would die of loneliness." They say of Frank, however, "Frank has so many original thoughts, his brain suffers from overcrowding"!
Eddie has a whirling dervish in his head.
If thoughts were sounds, he's have a cacophony in his head.
Shall I go on?
I can't think of a phrase, but you could use scatterbrained to describe your hypothetical person.
(of a person) disorganized and lacking in concentration.
A ROLLING STONE?
= A person who likes to move often or is unwilling to settle down in one place or with one person or both. This phrase is based on the old saying "a rolling stone gathers no moss."
"Papa was a rolling stone, my son. Wherever he laid his hat was his home. (And when he died) All he left us was alone."