I noticed that the players skins on the stats do not update.

i tried clicking the 'old skin? Refresh it now' .

But, it didn't work.

Is there some way to fix this?

The reason being is since the minecraft skin database is updated to 1.8, and there being no plugin for the updated version of a skin displayer, it will either give you a non-updated skin or a completely black skin

Late response, but both new and old skins are now shown properly. If you have changed your skin and want to update it on the website, go to your profile and click the "Refresh skin" link.

It shows the second head too. 

What second head?

The area around your first head. Like, the fringe on your skin and my hood.

That's intentional. I'll add an option in the account settings for each user to choose whether they want to show it or not.

Edit: Done, the option to hide the hair layer is now available in your account settings.