I noticed that the blue check means new posts, but is there a way of seeing of new replies without going through the posts? I don't always remember what was a new post that may have a reply added.

Yes, the Blue Check next to a Forum means there is a new post within that forum.

Once you open the forum and see the Topics, there should be a little box (can't remember the colour, will edit) next to the Topics which have New Posts in them that you have not read before. This is a cookie-based feature. Also, you can see the date and author of the most recent post within a topic to the right of the Topic line.