How do I figure out what module is using drupal_set_message()?
Are there any messages in your error log? You should be able to see a module name there.

drupal_set_message has no parameter to add a module name to the message so there is no straight forward method of finding the module. You could copy the string from the message and search in the translation page (if you have the locale module enabled. Or throw the string at Google and see what you find. That usually helps!