nnet() fit criteria

I'm using nnet() for non-linear regression as in Ch8.10 of MASS. I
understand that nnet() by default optimizes least squares. I'm looking
to have it instead optimize such that the mean error is zero (so that it
is unbiased). Any suggestions on how this might be achieved?

What makes you think least-squares does not achieve that?  At a guess you 
mean the average prediction error over the training data in a regression 
problem, and any non-linear regression with an intercept term achieves 
that.  But 'it is unbiased' needs futher statements including what the 
model is that what 'it' is supposed to be estimating unbiasedly in that 
model.

Now for a non-linear regression you should be using linout = TRUE (as in 
the reference you give), and then you do have a 'non-linear regression 
with an intercept term'.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595