I have enabled the internet sharing via Airport on Mac mini successfully. I can connect to the Wifi network from my iPhone but can't browse the internet. The problem might be that the Mac mini uses a proxy to connect to the internet. Is there a way to make this work?
First, try entering the proxy settings for your connection into the iPhone. You can do this by going into the Settings app > Wifi > Wifi network name > Proxy (which is at the bottom). Note, you cannot specify a .pac proxy file like this on the iPhone.
Unfortunately, this may not work. I had the exact same problem for me, and although it would work fine with my DSi, for some reason, my iPod touch hated the ad-hoc connection.