SharePoint can be viewed in mobile devices in several different ways. You can go with the OOB mobile view, which you can bypass in your device by manipulating the ?Mobile=1 (--> 0) parameter in the url. Or you can disable the mobile view altogether to bring the full experience to all devices, to the extent that it happens to work - mostly good for public facing sites meant for browsing sites, not working with e.g. documents.
But, who says you can't have both? I personally hate it if a website forces me to a mobile site when using my phone or tablet. Many times, all I want to do is browse the site, the full site, not a listing of libraries. Then again, sometimes that is exactly what I want. HTML5 may (or may not, can't know just yet) solve the problem of mobile views, but then again, will it push users, again, to a forced mobile view?
As for currently, I'm very much pro full site for everybody, and using separate mobile apps for the data browsing. In the Windows Phone 7x, there's the inbuilt Office Hub that does the job, providing straightforward access to the SharePoint library. The other platforms, iOS and Android, need a little help from the apps developers.
So on my iPad I needed to come up with something else. I found that the harmon.ie SharePoint app (Lite) didn't mind the https, and works fine. It doesn't seem to show all site content, only libraries (the full version might), but a plus for harmon.ie is that it provides easy access to my own MySite automatically.