As we see more and more public web sites being launched on SharePoint 2010, mobile support is becoming a hot issue on those sites. Depending on your approach, you may want to create a simplified version of your site targeted to mobile devices, or you may just want your site to render as normal on mobile devices.
The first approach of a targeted site I'll save for a later date. We've done this for one of the sites we built for CAMH at www.problemgambling.ca. If you visit the site on a mobile device, you'll see a significantly simplified site targeted to mobile. You can still reach the full site, but the default is the mobile version.
In the second approach you just want your site to render on mobile devices. In both scenarios actually, SharePoint tries to outsmart you to your detriment. It detects a mobile device, and tries to redirect you to SharePoint's mobile version. This really only applies to lists and libraries on collaboration sites, and typically gives a 401 Unauthorized on a public site.
To get around this, you can modify the web.config on each front-end server for the site. You need to add the following four lines just above the </system.web> tag.
<result type="System.Web.Mobile.MobileCapabilities, System.Web.Mobile, Version=188.8.131.52, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a"/>
While officially deprecated since the .NET Framework 3.0, this method still works fine.
Thanks to Koen Zomers for doing the discovery and posting about this at http://social.technet.microsoft.com/Forums/en-US/sharepoint2010setup/thread/d1e58832-391b-42ba-a21b-6ef40d1c9acb.