I'll say this another way.... the next page should NOT have Copy Thread in it, so something is screwing up the output of that page. That page should use the threadadmin_movethreads template and copying the thread is not an option in there. (There is no option to Mass Copy threads - users have been asking for this option for a while but it has not been added.) So, something is causing another template to be used on that page than should be used.
Do you have any sort of modifications that deal with moderation tools at all?
Does this happen to you at all? What happens if you disable your plugins - does it still happen?
Note: To temporarily disable the plugin system, edit config.php and add this line right under <?php
PHP Code:
define('DISABLE_HOOKS', true);