phpBB.com discussion: https://www.phpbb.com/community/viewtopic.php?f=556&t=2401321
On the phpBB 3.2 Support forum there are a number of reports of "weird forum output" and the resolution being to clear the browser cache (CTRL + F5) post upgrade.
This is attributed to the fact that as could be expected phpBB 3.2 introduces significant change to the underlying CSS files.
Since CSS changes can be expected between releases, particularly feature releases, the server side should be responsible for busting any CSS caching.
I'm not a web designer, but Google turned up idea such as How Do I Force the Browser to Use the Newest Version of my Stylesheet? for an example of how this could be accomplished.