Thanks for the replies. I can confirm that my server's Client Proxy Mode is correctly set to "Local Network Only".
QUOTE(Tenboro @ Oct 19 2009, 11:50)

You can try pointing your browser to [
192.168.1.20]
http://192.168.1.20:17171/ (or 127.0.0.1) and see what it says. If it gives any reply at all (normally a 404), you know that part of the connection is good. As long as it gets through to the client, you can look though the client logs for a more detailed explanation of what went wrong.
Okay. Tried that. I do indeed get a 404 as you describe, both for the loopback IP and for my actual local IP.
So I set my H@H Proxy to 192.168.1.20:17171 and tried browsing. Again, when I load a page I get only the name of the file as a hyperlink. I see in my logs, for at least one attempt, the following:
2009-10-19T21:43:37Z [info] {connId=18, rhost=/192.168.1.20} : GET / HTTP/1.1
2009-10-19T21:43:37Z [WARN] {connId=18, rhost=/192.168.1.20} : The requested URL is invalid or not supported.
2009-10-19T21:43:37Z [info] {connId=18, rhost=/192.168.1.20} : The remote host made an invalid request that could not be serviced.
2009-10-19T21:43:37Z [info] {connId=18, rhost=/192.168.1.20} : Writing httpResponse for GET: code=404 bytes=0
I also get a pair of lines following that indicating a failure to download favicon.ico as well.
This was, for example, trying to view
https://e-hentai.org/s/e28bc8e70605b2df0e...0-jpg/166055-21 which works when I don't set the proxy.
Looking at it, it almost seems as though the address part of the request is being stripped and replaced by a plain request to / (i.e. the root directory) but I don't appear to have any way to affect that.
Any suggestions?