Face Forward.......
Here was my reply: "Well first you can get all the faces to show the right way by going in the faces menu and then selecting "face to front" which will do exactly as it says. This will change your problem face from a black into a white. The selecting everything, duplicate the faces. And then on the duplicated section, in the faces menu use "reverse vertex order". That will make the other side visible. This way you don't have to move anything."

I'll explain it again in a little more detail, using the wings as an example.

Ok, so you've gone through the hassle of connecting the dots to make a decent set of dragonfly wings. It looks pretty ok. So in the blue 3D preview window, you uncheck the option "draw backfaces" and suddenly holes appear. The faces look wacky, mixed black faces, mixed white faces in there too. What the heck!?! You've connected the dots in every way you can think of, and nothing is fixing them. Something isn't faced the right way.

First, select the whole group. In the "Faces" menu up top, there is an option for "face to front". Select it. This will automatically make all those faces you have created in your wings face to the front.

Now, to do this the easy way to make a back for it, with the group still selected, go into "Edit" and "Duplicate Selection". Nothing will look diferently, but with that duplication selected, go back into the Faces menu and select "reverse vertex order". Now you will have a mirror of the original group. All set.

This is also useful if you are using parts of a mesh with another mesh, such as a skirt section, and the faces underneath disappear and make it look really bad on your sim. Duplicate the problem section and reverse the faces. Now the whole piece will be solid.

Also, if you still want the thin addition, and a different texture mapping on the back, you can now map them separately, since they are 2 different groups. Like an underneath section to the wings, and a back, like bird wings.