Looks like the default logfile location is in the same directory as the executable, but a regular user won't have access to write there. We should use either a temp directory or the %USERPROFILE%/.zenmap directory.
Example report with screenshot: http://seclists.org/nmap-dev/2016/q1/338
Py2exe is doing this: http://www.py2exe.org/index.cgi/StderrLog
It's capturing stderr and putting it in the logfile. Maybe we can override this; otherwise we'll have to reopen stderr somewhere else on Windows (like our own logfile)