IIRC, predominant right-handedness of human population has something to do with chirality (spirali-ness) of some protein molecules in our bodies. This chiraliness is also responsible for us being able to digest most forms of food. So unless we also consider most of the food (and in general biomass) on Earth having left-handed chirality, predominant left-handedness would mean that human diet is much more restricted (diabetes nearly universal, etc.). Bear in mind that this all might be complete bollocks, I'm no biologist.
Probably bollocks, due to my and others' first hand experience being left-handed and yet still able to eat normally.
Oh and the other major thing is that people will generally use their right brain more. Which doesn't mean anything as far as I am concerned, but apparently there are supposed to be big differences in what the sides of the brain do.