Yep, i see a problem.
In PS i don't find Join option for achor points.
But what would Brian Boitano do if he was here right now? 
1. Add anchor point on that central line (it does matter on which half it goes).
2. Press delete it (that should delete that point and one of central lines).
3. Select other central line and do step 1 and step 2.
4. Now click on one of anchor point (in upper middle or badge edge)
5. Move little pen tool and click. Can take few times to get right point. That will join those two points (not quite join but make path between them, making them on one path/shape). Better do it at maximum zoom.
6. Do it with others two.
Here how it looks now : [ATTACH]8429[/ATTACH]
Thats almost all you can do with it. Now it is one path/shape no holes no dublicated path/shapes. But still have two anchor points almost one on other.
I've would left that.
Of course, you can try and delete one of them but if you try you'll see that now you'll need to adjust angle and restore shape and no guaranty that new shape will be absolutly symetric.
Illustrator at other hand have "Join" option. But it have some restictions. And i didn't sucseed easy way. I had to delete central lines before "Join" started to work. So for that one no much diference where you'll do it in PS or Il.
