How do I override the taxonomy default content? I'm coding a way to display the taxonomy terms, and I don't want some of the term pages to report "There is currently no content classified with this term." I need to remove that message form the term pages with no content, but let the content be listed like normal when there is content associated with that term.
This information is added in taxonomy_term_page(). As you can see there, the page callback returns a renderable array, which means that you can easily replace it in a custom module by implementing hook_page_alter().

In that hook, check that you are on a taxonomy term page, look if the 'no_content' block exists, and if yes, override the #markup.

I suggest to use dpm() from devel.module to print $page so that you can more easily figure out  where exactly the page content is in that huge render array. Somewhere in system_main, if I remember correctly.