The bug

When summoning a slime with the Tag NoAI:1b it can still damage the player.

How to reproduce

1. /difficulty hard
2. /summon slime ~ ~ ~ {Size:3,NoAI:1b}
3. /gamemode survival
4. Walk into the slime and die a slimy death

Video: https://youtu.be/ZkI3uU7hoBA?t=2m33s

Fix

Having in mind the overall AI-System this is a hack. See note below.
There is a method canDamagePlayer() in EntitySlime.java. A check can simply be added there.

	...
	protected boolean canDamagePlayer() {
		// Added && !this.isAIDisabled()
		return this.getSlimeSize() > 1 && !this.isAIDisabled();
	}
	...

@EDIT I didn't find MC-67667 somehow. Searges comment declares it as "Won't fix".
I still think this should be changed as damaging logically would be part of the AI, even if it's not directly inside the AI code.

Note: As Torabi pointed out in his comment, this is probably not so much viewed as "Won't fix", but rather will likely get fixed properly in future by moving this part of entity behaviour to the AI-Code.
Looking at it, it looks like a simple task at the beginning, but soon you realize that it probably would make sense to relocate the EntitySlime in the class hierarchy and I think form there it will feel like this soon. It's understandable why it gets ranked less important than other issues for now.