It's debatable whether or not perfect pitch is a blessing or a curse. The Western tuning system (I can't speak for other tuning systems found in different cultures) is not perfect and in fact requires unconscious ear training before the music "makes sense." Ever listen to traditional Chinese music? It can sound pretty alien because our ears are not accustomed to their different method of slicing up an octave.
I read a great book in high school (given to me by my music teacher) called, "Temperament" and it detailed the history of how the piano came to its current form. It's quite interesting to see the weird pianos that were invented before its current incarnation was finalized (along with our tuning system).
Fascinatingly enough, early musicians had big problems while tuning pianos (or precursors to the piano, such as the harpsichord). They initially started with an absolute note (such as C) and tuned subsequent notes perfectly in harmony to this starting note. The result was that any piece in C sounded wonderful, but if the musician were to try to modulate or transpose the piece to an alternate key, the tones did not resonate very well and sounded like "howling wolves." After much struggle and experimentation, the final system that was decided upon (and is still in use in Western tuning today) is a system where an octave is equidistantly sliced into twelve parts. Because of this slight compromise in pitch (that is, the fifths, fourths, and octaves are no longer "perfect"), world-class singers and classical instrument players can purportedly have difficulty staying in tune with a piano.
My whole digression is to make the point that individuals with perfect pitch might notice all the little tuning inconsistencies that most people automatically and unconsciously adjust to the nearest expected pitch. I can't imagine being bothered by every little out of tune pitch I ever heard... not to mention I would probably get speeding tickets -- "Officer, I know I was doing 80 in a 65 zone, but my fifth gear RPM is exactly A 440 at 80 MPH and, well, I can't stand it when my transmission is flat."