Multisite domain mapping breaks CSS

This is an old question, but I just ran into this same issue and found the problem: the MU Domain Mapping plugin is using a deprecated constant, PLUGINDIR, to remap the plugin directories on the mapped domains.

The plugin seems to be very vaguely developed nowadays (and no releases have been out for a year), so I just edited my copy of the plugin directly. In domain_mapping.php for the domain_mapping_plugins_uri() function (around line 650), short-circuit that function by just returning $full_url without running through its other routines.

This should fix the problem.