Interesting, I have been having the same problem this semester. I am running Moodle 2.5.1+.
It doesn't happen for every post, in fact, very few.
My guess is that my server might be a little slow, and students click two times on the Post button, which Moodle then sees twice. It actually happened once to me, so I knew that I has clicked twice.
It might also have something to do with students using the Macintosh (which I use). On the Mac, you can go back by right-swipping the magic mouse or trackpad. I once did this accidentally, the swipped left, then submitted, and I ended up with two posts.
Hey, just for fun, I am going to click-click the "Post to forum" button (below) to see if my post to you gets recorded twice.
Since I now have a Mac, I also wonder if it has something to do with Safari?
We will have to experiment a little more. (Okay, here's my click-click, let's see what happens.)