Pick an image with a lot of high spatial frequencies, such as a three-pixel
square grid -- but any photo with strong, small features will do.  Select, e.g.,
the Polar Coordinates filter.  In the places where the image is shrunk, you will
see strong pixel aliasing and moire in the distorted image.  

This is because of the sampling technique being used by the resampling code.  If
the pixels are locally interpolated or sampled, then reducing the image will
result in aliasing.  Resampling correctly requires a variable spatial filter
that can average over suitable regions of the input image.  I have written an
algorithm that will do this correctly, as part of the PDL::Transform perl module
(http://pdl.perl.org); you can also download a scientific paper describing what
to do, from
"http://www.boulder.swri.edu/~deforest/Papers/2003-resample/resample-reprint.pdf".
A simple demo movie showing the benefits of correct resampling is at 
"http://www.boulder.swri.edu/~deforest/PDL/3gal.mpg": that movie shows the M51
galaxy, transformed to polar coordinates with periodic boundary conditions with
three different resampling techniques.

I regret that I don't have the time to port the PDL::Transform code directly
into the GIMP; but I'd be happy to help anyone who's interested in doing so.