Undirectional bursts of noise dampen out in the usual n^2 manner, and at the distance of light years becomes difficult to sort out from the undirectional burst of noise that we are pleased to call our Sun. Also, as noise, they don't yell out "intelligence!" as much as an analog radio signal, which is clearly from an intelligent source. Nuclear explosions may have some special characteristics, but frankly there's always something exploding somewhere out there in the cosmos. It's difficult to characterize the exact detection radius, but it's probably much smaller than you think.

Interestingly, as we become more efficient with our radio transmissions, which is to say, use less power, and ever more of it is locked behind at least one of excellent compression or encryption, it seems that the natural evolution of a civilization may return it to something that looks pretty natural again at a distance of light years. Dim, high-entropy signals once again become difficult to distinguish against background noise.

To be honest, the thing that yells "LIFE!" that is probably detectable out to a far greater distance than anything we humans have done is our oxygen atmosphere. We stand on the verge of doing elementary spectroscopy on distant planets ourselves.

Come to think of it, this is probably the most powerful argument against the paranoid alien. The paranoid, relativistic-projectile-firing alien isn't even looking for a sign of intelligence; the logic says they should extinguish all other life, just in case. But our planet has been broadcasting "I'm alive!" across the cosmos for between 1.6 to 2.5 billion years. If somebody out there was looking to preemptively kill everybody around them, they would already have gotten to Earth.

(Waiting until you can see a trace of intelligence is too late, after all, without FTL. In cosmological terms that's the striker hitting the alarm bell. You want to get there long before that. And even if you have FTL you're still safer preemptively neutralizing planets. Remember, it is trivial to neutralize a planet and reset its biological clock to zero; if you can wait a hundred years or two then very gently nudging a very large asteroid will do the trick, and if you're impatient there's any number of faster ways to do the same thing with very, very, very modest energy investments. Sterilizing a planet is easy.)

(On that note, no, neither the dinosaur extinction event nor any other impact would match this profile. An intelligence would successfully sterilize the planet, not merely "substantially stress the ecosystem".)

That's a great post, and yes, I was certainly working under the assumption that a nuclear explosion would have a distinct spectroscopic signature when compared to the emissions of our Sun. Is that false?

If we can (eventually) detect the oxygen atmosphere of a planet through passive spectroscopy, then it does seem to follow that we could easily detect nuclear explosions from the surface of that same planet. Unless I'm missing something...