The Seventeen Mathematicians

Once upon a time, the seventeen mathematics professors at a university
agreed that if any professor in the department ever discovered a flaw
in one of his own published papers, he would submit a typed letter of
resignation at the next weekly departmental meeting.  Each member of
the department had, in fact, published a flawed paper.  Each
professor's error was discovered and discussed by all of the other  
professors.  However, to avoid a rash of resignations, each professor
vowed never to point out a flaw in a paper to its author.  Thus, no
professor was aware of his own error.  Then, at the last meeting of
the year, a visiting mathematician announced, "There is an error in a
paper written by some mathematics professor at this university."  What
happened during the first seventeen weekly departmental meetings the
following year?  Of course, you can assume all the mathematicians
behave honestly and know that the other mathematicians are behaving
honestly (and logically).  Assume also that the professors attend
every meeting.

Supplementary question:  How did the visitor's announcement change the
situation, since every professor already knew the statement he made
was true? 

This is a (modified version) of an exercise in Chapter 1 of Michael  
Spivak's Calculus textbook.