Just had a reply from someone who managed to quote my text and then improperly extending it. I've managed to cut it down into the following demo: if you have a posting with this (wrongly used) BBCode:and submit it, phpBB will automatically try to rectify it by adding missing closing elements. However, it then turns out as: ...which will break the site's HTML severily, also breaking the style/design (see link).
Don't have a solution yet. It's unavoidable if someone really wants to break your site layout...