The subject line is an understatement...
Try saving a file with any transparencies either from Visio with the "Publish as PDF or XPS" function or via Adobe Acrobat. The results are not pretty.
Art
Yes, Art is very correct about this.
One failure of the pdf-export is with gradient fills that involve transparency.
I exported plain old gradient fills, and they seemed ok, but if there were transparent overlays, then the results were less than good. There is a very strong banding: