Link Start

 Well, we have never seen Nale using his heraldic powers, in order to know if he still has any (Tal seems to have some, but he might be different). I remeber reading somewhere in WoB that heralds can't surgebind without honorblades, and I don't remember reading any confirmation about whether the sword he carries is his own, one related to regrowth or a regular shardblade. And even if he was equally matched with Kaladin (surgebind but no extra powers useful for fights), he might not want take the risk.
 I don't know, it's just that he didn't seem display superhuman features reflexes that Tal did (catching darts in the air), he seemed quit unskilled at his appearances. I myself don't quite believe in this theory, 2nd possibility seems more likely, but I don't want to dismiss it either.

I always understood Kal's victory as psychological: he successfully undermined Szeth's will to fight. All he had to do was open Szeth''s eyes to reality: radiants are back, he was never truthless, he never had to commit those murders. He has no reason to murder Dalinar now, and he was only fighting Kal to get to Dalinar.

He despairs and dies.

A question that arises from the discussion of the onset of Kaladin's powers: why has Darkness never come after him? Don't tell me he never committed any crime. He was stealing from corpses to pay for safety bribes way back in Amaram's army. Later, there are all the times he attempted theft

Of himself and others who were legally someone else's property.

How would Nalan know about this? How did he know about Lift and Ym?

So, how come he never came after Kaladin (thief) Stormblessed, Shallan (double homicide) Davar or Jasnah (vigilante street vengeance) Kholin?

 I don't know if someone already answered that, but I don't have time to read the rest of the thread now, so, my theory:

Against Kaladin: Nalan is strong, but he is not invincible. Maybe he realizes Kaladin could beat him, if a 13yo girl can escape him and his men. Or maybe that has something to do with the fact that he is a slave, killing him would be destroying someone else's property, or that the bridgmen cannot be executed by anything else than refusing to charge at the parshendi, so he could not get authorization. Nalan appears to investigate the person thoroughly before taking action, he couldn't kill him right away;

Shallan: I doubt it would be considered homicide, it was self-defense and defense of others. He could, however, have come after her under the accusation of stealing Jasnah's Soulcaster, but even her (Jasnah) didn't know about what happened until the day of poisoning, and then forgave Shallan right after (thus dropping the charges). Also, the law of Alethkar wouldn't allow the execution of a lighteyes just for theft, so Nalan wouldn't be able to get authorization for this;

Jasnah: The book makes it very clear that everything she did in that event was completely legal.