Some responses...
"and the aliens can rightly conclude that while there is intelligence here, there's also a lot of brain-dead morons who think that the laws of physics only exist if you believe in them."
Well thats actually kind of true in some quantum theories. To observe a thing is to make it real. Do we create physical laws by observing them?
"Oh, here's another thought. Remember all those test nuclear detonations (along with two not so tests) we've set off. Gamma-radiation pulses are also kind of noticeable. Especially if the source is close by... Having nukes and the willingness to use them on a inhabited planet may not be the best thing to advertise to the universe at large."
Gamma Bursts tend to be fairly signifficant galactic events, no one really knows what they are but some speculate that they are stars becoming blackholes. Setting off a nuke at Bikini Atoll isn't really in the same ballpark. Its not even on the same continent...
Most people also seem to thing that life is inevitable, I tend to agree, however people get hung up on the great distances involved. What about the huge, mind boggling amounts of time involved? Its very possible that other life, will/is/has evolved in the galaxy, but the chance of it being in the same time-frame as us is tiny! How long do you think it will take for humanity to go "post physical"? Another 1000? 2000? or even 10,000 years? Thats an amazingly tiny amount of time to be around for. 1000's of civilisations might have lived and died/transended already and the only way we'll ever know is to dig up their planet lol.
Ofcourse this is only conjecture. But food for thought, none the less...