That could either be a cheap repaint job... or the 1st owner hardly ever washed the car, never gave it some wax, etc. Paint could have been burnt off from bird shit or something, along with little rocks hitting it while you drive fast which chip off tiny little spots and leaves white specks.

Is the clear coat gone? If it's not, try compounding it really good, and then giving it some wax. Meanwhile start looking around for a reputable shop that will paint it for you... and remember the golden rule... you get what you pay for.