I think that to get the default "New Forum Posts" block to parse BBCodes, a core file would have to be edited. I try to avoid this whenever possible. If you set about editing your core files, then these edits have to be made each time you upgrade vBulletin.
The other alternative would be to create a custom forum block that roughly duplicates the default block's function, and then you could manipulate the post text however you want, including calling the BBCode parsing function and handling potentially orphaned tags if you choose to truncate the content. Another alternative for long posts would be to put the post content in an element with a maximum height, and a vertical scrollbar is introduced as needed.
Let me know your thoughts on these issues, and I will see what I can do with it.