Ok lets see if I can get a handle on this, I will put on my old QA hat and see if that helps 
Problem 1 - QT editor buttons do not work when trying to edit a post, but work fine when creating a post.
Right I have in my profile Visual Editor checked off in my wordpress profile and also have use Quicktags Editor checked on in the forum options, this is what I believe to be the state that Andy mentions. However I have checked the Visual Editor on in my wordpress profile and I still get the same thing happening, unable to use the buttons in the Quicktag editor when editing a post but fine when creating a post. It would seem that you guys already know about this problem however so I will await the fix.
Problem 2 - Target code gets appended onto link code whenever a post is edited, sometime resulting in several iterations
Ok whenever I go to edit a post that contains an already existing link then the target=”_blank” gets added to the link code.
eg. If I create a post with a link to the homepage in it the code generated it as follows
<a href=”http://www.defconsoft.co.uk>Text</a>
If I then edit this post when the editor opens up ready for edit the code looks like this
<a href=”http://www.defconsoft.co.uk” target=”_blank”>Text</a>
If I save this and edit the post again, another iteration of target=”_blank” gets added for everytime I edit and save the post
<a href=”http://www.defconsoft.co.uk” target=”_blank” target=”_blank”>Text</a>
If you look at the source of the forum post here you can see this happening in the links within the posts. I am guessing this is probably an after effect of the 'double editor' issue perhaps?
Problem 3 - TinyMCE editor not even creating link code
Right problem three is not as important to me as I tend not to use the TinyMCE editor on my site, however when I did try to use it to see if it fixed this problem I could not actually get it to work in generating the link code.
I would type out my post, highlight the text I wished to place the link onto, clicked the Insert/edit link button, filled in the address, the target etc, clicked ok and the text did not show as a link (underlined etc). When I looked at the html for the link it came out looking like this.
This is a <a href>link</a> to another side
Or in other words it did not add in the web address or target that was entered into the pop up box upon clicking the link button. However now that I think about it this looks like it could be due to a double editor problem as well.
Now hopefully that explains it a little clearer and if your previous answers are still relevant then please disregard this post, I just wanted to make sure I was clear in reporting the issue so as not to cause any confusion.
Cheers
Defcon
PS. Hope this comes out formatted ok 