I was making a flying machine and decided to attach fences to the slime blocks (so I could attach a horse, ride it, and be dragged by the machine; it's on a superflat world). I'm on 14w21b.

It only happens while the block is moving. Instead being fence shaped and holding leashes, it transforms into a (oak) wood plank in shape, and drops the lead. An easy way to reproduce these glitches is to set up a sticky piston with a slime block and a redstone block attached, and wire redstone to connect the redstone block to the sticky piston. It should start switching each tick; always in motion. Then just attach different blocks to the slime block.

I figured out that this happens to things that use a "parent" texture, such as stairs, slabs, carpets, cobblestone walls, etc.

After more testing, I found that texture glitches happen on blocks with orientations, such as hay bales, logs, etc. They switch orientations.

These first two groups share a common quality: they say "round trip different" in F3 mode (and sometimes in purple, other times pink letters) when you look at them moving. I don't know what that means.

I also found that some blocks are not movable by Slime blocks, such as beds, chests, paintings, item frames, etc. Item frames & paintings will stay if they are supported by another block, but fences, pots, signs, vines, etc break as soon as the slime block moves.

The fact that Slime Blocks don't move beds (and break signs) may be intentional, but what's happening with Hay Bales and fences and such are certainly glitches.