When users click on the quick reply button it then by default makes a reply to the last person who posted.

This is confusing people as to who is replying to who. I would suggest removing the "quick reply" function so that it then becomes apparent exactly who we are addressing.

Yes, I find that confusing too.

Perhaps there is a way to change a default setting, so that quick-replies appear in their correct thread position?

Yes. That would be a solution, Rev. Entity.

It would also be necessary for it to state the right person in the bar at the top of the post - as it currently is, that is also wrong and is causing misunderstandings.

Perhaps it would be possible to do away with the Quick Reply box altogether when viewing a thread in flat mode.