The Zombie-on-Death + Stoner thing is intentional. Ways of dying are not discriminated here, as long as you're not meaning "if it's already a zombie, then passes through a slowfreeze, then gets stoned, a second zombie emerges". It even applies to traps that, graphically, would reduce the lemming to nothingness (and applying it with triggered traps was the most difficult in terms of coding).
Will look into the others.
EDIT:
> Climber bug - This actually applies to all skills! Oops. That's what happens when I don't test thoroughly enough. Fixed for -B update.
> Instant Pickup Skills + X on assign gimmicks: That's debatable, you could argue that since the player isn't directly assigning the skill, it shouldn't happen. What's happening from a technical point of view is that, these "X on assign" effects don't happen while the skill counts are frozen, and they're frozen while the lemming is given the just-picked-up skill (to avoid the skillset being reduced, or the skill refusing to function if it's not in the level's skillset). So in a way, yes, it's a bug, but it's also one that perhaps the outcome is how things should work anyway.
> Instant Pickup Skills + bomber/stoner: Fixed. Also fixed the one-frame delay before they actually explode/stone.
> Instant Pickup Skills + replay: As long as this doesn't cause any other glitches, I'm not worried about this one.