Several entities seem to have rendering issues where some or all of the entity is rendered invisible. Specifically:

Spiders: Legs and eyes are visible, but the body is transparent
Zombies: Completely invisible, a very serious issue!
Squid: Body and half of the tentacles are invisible
Chickens: Unsure. I haven't seen any in my 1.4.2 world, so they might be invisible.
Chest: Lid or body of chests and enderchests rendered invisible.
Signs: Sign rendered invisible, text remains. (Possibly only with Optifine, have not yet seen in Vanilla)

I have not yet seen any Endermen, Cave Spiders, Blazes, Villagers, or Zombie Pigmen. I do not know if they are effected. (CORRECTION: All mobs are effected)

UPDATE: After updating Java and LWJGL, the bug is not fixed but far more random. The previously effected mobs now have random parts missing.

Attached screenshots. The burning effect you see is actually fully-invisible zombies burning in the sun.

UPDATE 2: For reasons that I cannot fathom, either carelessness or system error, this has been marked as a duplicate of MC-61 and resolved. This is not the case. I never made any mention of invisibility potions, and this bug still exists as of 1.4.7. There is no point in this amazing bag tracking system if Mojang isn't even going to read the bug reports, and just classify them as resolved because they supposedly duplicate other, completely unrelated reports.