The bow seems to be upside down when in 3rd person view. It is less noticable with default textures, but when I loaded a custom texture which replaces the bow texture with a slingshot texture, the bow was upside down in my players hand, but looked absolutely normal in my hand when I switched back out of third person view.
As you can see in the image I have added, the bow (slingshot texture) in a normal hand is normal, but the bow in the skeleton's hand looks to be upside down.
I can't notice a difference with default texures