Suppose someone played perfect chess (in some weird technical sense). What rating would that translate to using the current Elo scale?

What would the ratings be if the "Perfect Chess Player" played as White or Black only?

Nobody knows for sure, but there are lots of opinions! For a summary of the issues, these are quite good:

http://en.wikipedia.org/wiki/First-move_advantage_in_chess

http://en.wikipedia.org/wiki/Chess_engine#Chess_engine_rating_lists

Great Stuff, fburton! Thank You!

You're welcome.  I realize those links don't address your questions exactly, but they at least give a clue why they're not so easy to answer.

Oh, I never expected a clear and concise answer. The Wiki article on the first move advantage was very interesting and well written!