There's thing in here you're simply overlooking from lack of familiarity, the 25,000 gigatons of atmosphere Mars has versus our own five million makes it pretty redundant what the current make up is, the existing atmosphere is effectively nil from our standpoint.

Also you can not simply assume a land ratio of 100:28 means you need 28% of the air, that's not how it works, if you want land people can walk on you need a pressure of 14 psi, and that means pounds of air, not mass. So in reality the 5E15 tons of air is accurate if its weight not mass, the mass you need is adjused then for the difference in gravity and kicks up to 13 million or 28% thereof for 4.7 million gigatons. For equal pressure, Mars with it's mere 28% of Earth land surface needs over 95% of it's atmospheric mass. You get that from a lot of comets or you get that by baking the ground for oxygen and CO2 that can be turned to oxygen through classic plant biochemistry.

Now greenhouse domes is one option, and a more probable one if you feel there's enough native nitrogen, oxygen and hydrogen. Even in that variation though you are using mirrors and lenses to bake oxygen rich minerals for their oxygen and/or carbon dioxide. But you're now limited to -barring fusion or von Neumann machines - slowly leaking gas out of the domes as you make it inside them by baking the stuff out of the soil through solar power which is noticeably weaker on Mars. Nuking the place isn't presented as the best option merely one that does produces a very rapid effect. Several megaton nukes accomplishes that same goal very quickly and with material we can economically move to mars, a single nuke would probably have about a total effective cargo mass as a person since no food or air or such need travel with it. Christ knows the mass on dome parts for even a single acre and I'd be willing to bet a couple hundred acres of dome wouldn't accomplish the goal in even geological timespans. Doesn't mean I'd do it that way but it's a realistic option and you shouldn't be knocking Sagan for suggesting it. You can nuke the fucker then build domes, easier if there's already some pressure on the outside.

Now getting back to the moon, I am not and never was worried about the contaminants as I said right form the outset, I was explaining that the dust would land all over the moon. From a scientific standpoint that's crappy because the moon is our best source of geological data for the solar system, especially before we went their, that's the 'problem' form the scientific standpoint, you couldn't isolate such a blast and you'd get a thin layer over every damn thing which while not really a big deal to us now would have been - before collecting samples - the equivalent of someone offering a forensic scientist to go in and clean the crime site in advance with bleach.

Mars would be a different story entirely, you're not talking about setting off a handful of nukes. You're probably talking about needing the equivalent of a ton of explosives to get a ton of air, or in that general magnitude, so if want 5 million gigatons of atmosphere you need to deploy around that in nukes... some high hundred of millions megatons of explosive, or low billions, maybe even double digits. Hence entire planetary supply of nukes presumably re-calibrated as super-high yield H-bombs, all Castle Bravo on crack. Hence why I did use the term 'irriadiating' when I brought up Mars. Odds are that sheer amount of detonation would have so much dust in the air that the heavier elements, the left over fissile material, would be buried in several feet of dust and if it's all plutonium, half life of a thousand years, it wouldn't be too big a deal in the medium long term.

Now as to that last bit about shooting nuclear waste into the Sun, that's just never made sense ever, I don't even know why that keeps going around.