On a WordPress MU installation, it is not possible to configure the favicon for each site independently within the single mobile theme. You are advised to create multiple derived themes from the mobile base theme, and configure the favicons separately for each.
Note that if you use a desktop theme that provides unusual, additional page templates, the default mobile theme will not have the corresponding logic. The mobile theme will fall back to showing a default posting list. However, you are able to create new mobile templates just as for the desktop theme. (Copy archives.php as a simple example of an auxiliary page template.)
If you are using a desktop domain and a mobile domain, it is not currently possible to host them on different sub-directory locations (eg http://mysite.com/blog/ but http://mysite.mobi/). Both versions of the site must either be at the top-level of the domain or in the same sub-directory.