Mobs / Other players only looking in one direction / walking backwards on SMP

What I expected to happen was...:
Mobs to look around as normal

What actually happened was...:
Most mobs are walking backwards, sideways etc.

Steps to Reproduce:
1. Start minecraft
2. Look for mobs
3. That's it!

Here's a video of it happening:
https://www.youtube.com/watch?v=x1mbERWEMr4

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Other players in SMP only turn the head, the body stands still
Affects also the player model in inventory (MC-34921)