I can't believe nobody's submitted something about this yet... if someone has, feel free to merge it. I know that there are other problems with hattish mobs (like being deleted).
A number of mobs that are supposed to ride on your head have various issues:
-Try putting a turtle on your head, mounting a mob, and traveling a couple hundred blocks. Did the turtle snap off of your head and go back to where you found it?
-Try putting a bird on your head and rapidly releasing and catching it again. All of its interactions should stop working. You can't pick it up or punch it.
Also, you can sleep in a bed and any mob that's on your head will stay there... sort of. They'll be in a weird place and act very buggy. They should probably be ejected or something...
I have videos for both of these bugs, but I need to send them from a computer that actually supports screen recording.

Similar issues were reported in #147 and #150, we might rework the entire picking up mechanics at some point.