I am having an issue doing Facetime between my parents' iPad 2 with my iPhone 4. Both sides stuck at "Connecting..." until we hit the disconnect button.
The same iPad 2 can do Facetime from my brother's home WiFi to my iPhone 4 without issue. What is special with my parents' home network is that it has a Webserver running and therefore their WiFi router has set up to forward port 80, 443 and another application port 3389 to the Webserver machine in the private network.
Checking online, I found this Apple tech notes about port forwarding. So I stopped forwarding ports 80 and 443 for the Webserver but the issue still remains.