Hmmm. Well, my first thought is that Undead = powered by negative energy. So he'd probably retain the Cure = damage, inflict = cure aspect, at the very least.
Since having a Con score would imply it can be damaged, he'd probably still take ability damage/drain from a source other than negative energy (which would make sense; he still relies on his tendons and muscles for movement, for example, so an effect that hindered his muscles/tendons/joints would still work, but since he is healed/empowered by negative energy, something like Wail of the Banshee probably wouldn't).
By that logic, crit immunity is out of the table, definitely, but partial fortification could still be there, as Agita pointed out.
Poisons and diseases would probably have no effect, as I don't see him as having a metabolism (no pulse, no breathing, no need to eat). Perhaps more accurately, he doesn't NEED one. He could force his heart to beat to simulate a pulse, or force his digestive system to work so he could enjoy a meal (In case you're wondering, part of the idea behind this comes from Vampire: The Masquerade), but it'd be a conscious effort.
I'm not sure about mind-affecting effects, though. I thought only mindless undead were immune to those?