The little LCD TV I tested the Raspberry Pi with wasn't very good, so I wondered if it was possible to remote into the Raspberry Pi from another machine. I found that this is no problem when I looked here. So I tried the following commands:
sudo apt-get install tightvncserver
...on the Raspberry Pi and it worked perfectly. Then with a copy of the TightVNC client running on my windows machine, I can access the Raspberry Pi remotely. This is awesome.
I used that approach to do more testing of my simple C# webserver, so here I am testing the webserver in TightVNC ... and also checking that the page is being served over my network to the PC in internet explorer:
...and finally, here is the Raspberry Pi serving the same test page to my iPhone:
OK, that all seems to work. I've just got to figure out what to do next now.