I am not exactly sure how hard this would to be to achieve or how much server resources this would require but heres my idea:
Have the “All Unread Topics” page automatically update when a new post is posted. It would just appear on top and move everything down - I know its not too hard to refresh the page but just an idea 
I disagree, that’s a terrible feature. I don’t want to click on a thread only to have clicked the wrong one due to the whole list shifting down.
wouldn’t you notice it shifting? ???
They already have a notification that shows up on any page when there is a new thread. I think that works pretty well.
thats not what im suggesting here though
Yes, I know. I’m just saying, in my opinion I think that works better than what you are suggesting. In your scenario, it seems like you are always staring at the new posts section just waiting for…well, a new post. The way it is now, you can browse about the forum and you are notified when a new post is in.
would both be bad?
EDIT:
I understand if this is too minor of a thing to waste Riven’s time on