The problem with this approach is that it requires the forum software to maintain state, whereas it currently has no notion of state or history. The page is generated via a query, where some post timestamp is >= the specified timestamp of the "active topics" dropdown (this defaults to "last login").
It's not a trivial problem, but could potentially be tricky to add. See, you're requiring the forum software to remember the result set from the previous 'active topics' query, and compare the entire result set with the current result set to spot additions.
This result set could be stored as some serialized array in a server-side session cache.
The other (and imho better) solution to this problem is to only save the timestamp of the last active postings display, and write a query that performs the set differences for you.
Problem is, this depends on your database's ability to perform such queries.
When all is said and done, it seems to me that it's all a wasted effort since you can just view the topics that have been active in the last 15 minutes. It should be pretty easy to tell if any postings are new, since you're not really going to have THAT much activity happening in a 15-minute window.