My thread is closed, so I use this thread.
I think that I found the reason why sometimes I see double post (for me it is very rare occasion). But, when I say that I see double posts, this doesn't mean that there are actually made double post, they just look so on the screen.
Thing is, as I understand it at this moment, we have two ajax systems at the work when we use quick reply.
First system is original vB, it uses ajax to just append new post when we use quick reply. Post just "appears out of nowhere" in thread.
Second system is from Ajax threads, that works similar to this system, posts appear also "out of nowhere".
And, if by any chance both system work at the almost the same time, there you can see double post, but as I said, it doesn't seem that there's actually double post in DB, only on screen. If thread is reloaded (standard way), there's only one post. So, this is, at least for me, just visual problem and not that big.
As it is connected with "synchronicity" of these two things, having Ajax thread that refreshes very often can cause more double posts. I use 10 seconds on my site. If you want to try test it some more, try with 1 second and write with quick reply, I'm sure you'll be able to catch at least few "double posts".
Of course, I'm not 100% sure, but I just had one and I think that I saw "blink" of Ajax refreshing my screen, that lead to double post.
Hope this will help you to understand what is going on and even maybe correct it, although this is not too big of a problem for me.