Assuming the dirt weighs about 2 tons per cubic meter, this corresponds to 58 kg/m^2 / 2000 kg/m^3 =~ 0.03 m, so it seems like the gp just used the incorrect unit.
You are correct. I had 1000000000 as a trillion. Scientific notation is a much better way to calculate things. At 30mm that is a big enough layer that a geologist could see it in the rock record, if it looked different enough.
I believe that we've spewed enough radiation that no visual distinction would necessary for detection, at least for the next several tens of thousands of years.
It's true that atmospheric nuclear testing has produced trace elements that were basically never on Earth before 1945, like Strontium-90 [https://en.wikipedia.org/wiki/Strontium-90]. Strontium-90 has a half life of about 29 years, so it will be detectable for a few thousand years or so. Some others last longer.