When mooshrooms are walking around, you can see the mushrooms on their back z fighting.
Steps To Reproduce:
Spawn several mooshrooms
Observe their texture closely as they mooove
Attached screenshot gives an idea of the glitching textures to look for.
(Regression, this was fixed in an earlier version MCPE-8471)
This appears fixed in 1.0.0
(There is a small amount of z-fighting when the mooshroom's head is at certain angles, but I don't think it's enough to keep this ticket open)