Some time ago I finally noticed that my Lumia could indeed be used as a wifi hotspot. I vaguely recall trying it out successfully with my laptop, but didn't really have the need for it after that. Except for with my iPad in the bus, and that didn't work. I thought the problem was somehow related to iPad being unable to use the network via Lumia or something.
This Monday I realised that the problem was something deeper than that. I needed, truly needed, to use my Lumia 800 as Internet connection for my work laptop. And it didn't work. I got a connection, but could not open any web pages or connect to Exchange. I tried to use our office VPN connection, but it would not connect either. As my last resort, I tried our home VPN. And that actually worked! And started tunneling requests so I could access web sites and my email, too.
Turns out for some reason Lumia did not provide any DNS service to my laptop, or iPad either, and that was the reason for nonworking networking. Our home VPN is confugerd with an IP address on my laptop as well as iPad, that's why it functions when using my Lumia for Internet connection.
Whether the problem is caused by Lumia or my mobile provider (or the combination of those two), I don't know. But at least I do know how to work around the problem. An IP address configured VPN connection does the trick.