Add mime types with plugin

Obviously your plugin is producing an error!

More specifically, those allowed mime types are called in such a way that this error happens before WordPress actually starts sending output. The result: an error message get’s printed, then WP tries to send its headers and your error happens.

Try this:

<?php
function wpse35410_new_mime_types($mimes) {
    if( ! isset( $mimes['pdf'] ) ) $mimes['pdf'] = 'application/pdf';
    if( ! isset( $mimes['zip'] ) ) $mimes['zip'] = 'multipart/x-zip';
    // etc.
    return $mimes;
}

I could be totally off here, but I suspect that’s it. I was not able to reproduce the error with your code, so I’m not 100% sure.