The developer of NmapFE for OS X hasn’t made a release since late 2004 and consequently is using an outdated version of Nmap. Outdated to the point it doesn’t work:

sendto in send_ip_packet: sendto(5, packet, 28, 0, 127.0.0.1, 16) => Invalid argument
Sleeping 60 seconds then retrying

I’ve created an Intel build from CVS using nmap 4.20, which seems to work for me. It is available for download here.

Update: Actually, this doesn’t work very well. I’ll compile something soon that does.