From a PHP point of view, it is no problem registering multiple shutdown functions. So it must be something special Wordpress does, that prevents Fuel's shutdown function to kick in.
And that is a bad thing, because there is a lot happening there. If that doesn't work, sessions will not be written (and this causes your messages issue), file downloads won't start, there will be no cleanup, the finder file cache will not be created, etc.
A quick peek in the Wordpress code shows that it's shutdown code calls the 'shutdown' hook, which processes shutdown events from installed plugins, and it calls wp_cache_close(), which since WP 2.5 is a noop. But again plugins can implement it.
So it looks like one of your Wordpress plugins is doing something very nasty...