I have two fields that are required and one interest group. I kept receiving an error message from MailChimp (via your API call) that "FNAME" (first name) was required when submitting the subscribe request via your module interface. I tracked the issue down to a bug where this information was not being passed to CmcHelperRegistration::activateDirectUser(). See the following graphic and associated hack:
CmcHelperRegistration::activateDirectUser() expect the arrays cmc_groups and cmc_interests to be children of cmc (as 'groups' and 'interests'). I am using Joomla's registration process.
*Edit* -- graphic above was poor quality once submitted... here is a smaller cut and hopefully more legible. The PHP module in question is plugins/user/cmc/cmc.php.