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.
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Please provides some screenshots for confirmation.
It seems like the mobs are affected by the new potion ''Invisibility potion''..
I have no idea.
Not sure how valuable pictures of invisible things are, but I have uploaded screenshots.

Duplicate of MC-61

Ok, Reopened.

I have also had this occur, but only when using optifine. Do you have any mods installed?
I do currently use Optifine, but the error is visible with and without Optifine. When I use Optifine, I also have trouble with entity textures being randomly replaced with terrain.png and random masses of polygons randomly filling whole chunks. That much is clearly Optifine's doing, and is why I hope Optifine will become obsolete after 1.5.
I would update my graphics drivers to see if that fixes the issue, but Intel does not acknowledge this model of graphics adapter anymore. Also, the issue is only on Ubuntu Linux. I have tried updating LWJGL, to no effect.

Can I also assume you are using fast, and not fancy, graphics?
That would be correct. Updated Environment accordingly.

Can you specify all of your video settings? I cannot seem to reproduce this without optifine, though I can confirm that this only happens in Linux.

Please force a crash by pressing F3 + C for 10 seconds while ingame and attach the crash report here.
Incomplete.
I changed to the standard version of optifine and it fixed this exact problem on ubuntu version 13.04. I hope this helps.
I have also seen this happen with armor stands, either being completely invisible or rendering only the base at an odd angle (I believe this to be the entity's "feet").
Updating my drivers and/or the d snapshot seemed to fix it for me.

@@unknown: Can you please try out with 14w32a/b/c to see if that was your driver or the snapshot ?
And please force a crash by pressing F3 + C for 10 seconds while in-game and attach the crash report ([minecraft/crash-reports/crash-<DATE>-client.txt|http://hopper.minecraft.net/help/finding-minecraft-data-folder]
) here.
This is a forced-crash report after I entered my world in 14w32b (the version of minecraft I was having the visual bugs in). I updated my video card drivers before entering and the problem was fixed.

OpenGL: AMD Radeon HD 7660G GL version 4.4.12874 Compatibility Profile Context 14.100.0.0, ATI Technologies Inc.
You don't know what driver version you had prior to this ?
@Kumasasa Looking at previous crash reports, I think it might be version 4.2.11476

Ok thanks. That was Catalyst 12.something.