I was watching a villager (farmer - buys wheat &c) when the villager suddenly "glitched" downward and vanished through the completely solid ground, never to return.

I was also watching when a sheep walked directly through a solid fence.

Entities walking through solid blocks seems to be very common. I have tested this by using a double-row of fences to enclose my animals, with a one-block gap between the two rows. I often discover entities caught between the two fences, where no mob should be able to go.

I also have discovered a rabbit inside of a house, and the only way for it to get there was through the solid walls, not via the door.