
   If the Papacy is infallible, and this is a matter of faith, then the 
   Pope cannot "be wrong!"  If, on the other hand, this is not a matter 
   of faith, but a matter of Church law, then we should still obey as the
   Pope is the legal head of the church.

   In other words, given the doctrine of infallibility, we have no choice
   but to obey.

This is a primary problem in the Church today.  What you are saying is
more or less heresy.  You might call it "infallibilism".  It's the
idea that the Pope is always right in everything he says or does.
This is virtually all over the place, especially in this country.

The Pope is only infallible under certain very specific and
well-defined conditions.  When these conditions are not met, he can
make mistakes.  He can make *big* mistakes.

A couple historical examples come to mind.

Bishop Robert Grosseteste was perhaps the greatest product of the
English Catholic Church.  At one point during his career, the reigning
Pope decided to install one of his nephews in an English see.  Bishop
Grosseteste said that this would happen over his dead body (though
maybe not in so many words; you have to treat Popes with respect, even
when they are wrong).  The problem was that this nephew would just
collect the income of the see, and probably never set foot there.
This would deprive the people of the see of a shepherd.  Bishop
Grosseteste was quite right in what he did!

Another example is that of Pope John XXII, a Pope of the Middle Ages.
He decided that souls that were saved did not enjoy the Beatific
Vision until the Last Judgement.  He decided that this should be a
defined doctrine of the Church.  Though he didn't quite get around to
defining it.  Now there's no way this is compatible with Catholic
doctrine.  The Pope's doctrine was criticised by many in the Church.
He went so far as to put a number of his opponents in jail, even.  In
the end, he had to admit his mistake.  Shortly before he died, he
recanted.  His successor made the exact *opposite* idea a dogma of the
Church.

If you consult any of the great Catholic theologians who treat of such
subjects, such as St. Robert Bellarmine (a Doctor of the Church), you
will find detailed discussions of whether the Pope can personally fall
into heresy or schism.