It may be my mistake, but I often find new posts in old threads even when they are marked "No new posts since you last visited."
I think what may be happening is that this function operates for the site as a whole, not for each separate forum. In other words, when you log off of the site, every post in every forum up to that point is treated as "old", no matter which forum(s) you actually visited. This can be confusing if you don't visit the same forums each time you log on. In that case, the "No new posts" indicator isn't very useful.
Unless I'm getting this wrong, may I suggest that the "No new posts" indicator be changed to operate separately for each forum, rather than the whole site at once.
Am I missing something?