When I joined my server (hosted on the same machine I was running Minecraft on), I gave myself a custom player head (/give [me] skull 1 3

), and when I put it on:
a) My inventory disappeared; no highlight appeared when I moused over an 'empty' space, but if I clicked once and closed my inventory, the item in the space I clicked was dropped on the ground like normal.
b) Entities (including players and my armour) and blocks with tile entities glitched hugely; they moved around and flipped upside down, depending on where I was standing, where I was looking and what perspective (F5) I was in.
c) No head appeared on my player model, either in the inventory or in the world, to me or to other players.
However, skulls with no NBT data (creepers, skeletons, wither skeletons, zombies, even Steve heads) worked perfectly, with no issues.