As the title states, the item sprites for the bow and the bow's drawing animations, are upside-down when viewed in 3rd person.

(When using the default textures, it's not very noticeable. The only cue to this bug with the default look is that, when drawn, the bow/arrow looks slightly higher on the arms. Not lined up.)

Skeletons also hold their bows upside-down.

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In the photos given, I am using a texture pack of mine that has swapped the bows for scoped crossbows. The scope is on the topside of the item, but when viewed in third person, the scope is on the bottom. The skeleton is also holding it upside-down, as well.