One serious, and very likely, problem that would be a result is a war. It is not unlikely at all that a extreme militant anti-biomodification group would arise - trying to kill off any modified humans they find, blowing up engineering clinics, ect. all in the name of keeping the human race pure. And eventually the modified people will fight back - likely with technology more advanced than the 'naturals' since they'll be more intelligent and thus better able to design such things. If the war didn't go nuclear, it would be a long, bloody struggle for survival that would make the extremist Islamic jihad against the U.S. look like a food fight.
You ever play Deus Ex 2? Your analysis sounds very similar to the entire plot/theme of that popular game.
