Interesting about the trailing slash not making a difference. Because in terms of the headers Apache sends (and I don't have a proxy between me and server) differs quite significantly:

curl -i http://4-ch.net/dqn/mobile
HTTP/1.1 200 OK
Date: Sat, 22 Dec 2007 08:58:02 GMT
Server: Apache/2.2.3
Content-Location: mobile.pl
Vary: negotiate,Accept-Encoding
TCN: choice
Transfer-Encoding: chunked
Content-Type: text/html; charset=shift_jis

Now see above, I thought it was the Content-Location or in fact the TCN header that might have been stumping it, because, looking below...

curl -i http://4-ch.net/dqn/mobile/
HTTP/1.1 200 OK
Date: Sat, 22 Dec 2007 08:58:41 GMT
Server: Apache/2.2.3
Vary: Accept-Encoding
Transfer-Encoding: chunked
Content-Type: text/html; charset=shift_jis

All of those potential problems aren't present when we trail with slash. This makes little sense. Let's start looking at headers from static pages:

curl -i http://4-ch.net/mobile
HTTP/1.1 200 OK
Date: Sat, 22 Dec 2007 09:11:11 GMT
Server: Apache/2.2.3
Content-Location: mobile.html
Vary: negotiate,Accept-Encoding
TCN: choice
Last-Modified: Fri, 14 Dec 2007 00:07:42 GMT
ETag: "1dc165-8c2-d9ea6f80;38f78f00"
Accept-Ranges: bytes
Content-Length: 2242
Pragma: no-cache
Content-Type: text/html

So browser has no issue requesting this page, which is also being "manipulated" by MultiViews like the addresses above. What I can deduct from this is that firstly the client is to blame for all of it's own problems, and secondly, it's sending headers or something it shouldn't. Multiple choice requests shouldn't be occurring. Request http://services.4-ch.net/tools/headers and then do another request with the .pl, remove the IP/host bit and paste me the rest. I'd like to see exactly what's being sent.