Here's what I do:
Put this in the browser menu bar:
Log in to the site by clicking on this link. The forum will ask you to log in as normal, them immediately present you with a list of postings made since you last logged in. Scan this list for anything that interests you. Refresh the page or hit the link again to have the "I've read this" flags updated as you work down the list.
Log out in the normal way. When you next log in by the same route, the forum will once again give you a list of only the new postings.
If you want to browse without resetting the "New Posts" time, don't log in, but browse the forum as an anonymous user. I've set my loged-in persona to use a different colour theme (blue) so I always know whether I'm logged in or not.