The bug
When shooting with a bow held in the offhand while in third person it looks like it's pointing towards the ground and there is no hand animation.
The picture on the left is the broken animation in the off-hand. The picture on the right is the animation in the main hand.
How to reproduce
Take a bow
Put it in the offhand slot
Try and shoot with it
Code analysis
Code analysis by @unknown can be found in this comment.
Confirmed for 15w37a