It is quite obvious that you did not open and read the links.

Or alternately you are unable to associate one event with another.

But since you are challenging my assumptions I will try to clarify my position to you.

You said:

Do you even know what "kinetic energy" is? It does not sound like it.

I am quite certain that it is the same today as it was in the beginning of the universe.

From Wikipedia, the free encyclopedia
Kinetic energy (SI unit: the joule) is energy that a body possesses as a result of its motion. It is formally defined as the work needed to accelerate a body from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude would be required to return the body to a state of rest from that velocity.
Under certain assumptions, this work (and thus the kinetic energy) is equal to Ek = 1/2mv2 where m is the object's mass and v is the object's speed.

By using the words, "accumulating kinetic energy", I was hoping that the reader would understand that there is an "accumulation" or increase in the motion of air molecules and that increased motion is "stored" in the atmosphere until the molecules impart their "kinetic energy" to other molecules that have lower "kinetic energy", or alternately as I implied elsewhere, the fast moving molecules could escape the Earth's gravitational influence and be lost forever.
I hope that this explanation clarifies to you my understanding of kinetic energy, when applied to air molecules.
Do you have different interpretation or understanding of "kinetic energy"?

I am not in total agreement with you when you say:

The atmosphere is in dynamic equilibrium with the Sun as primary heat source (along with tiny amounts of geothermal heat) and the cold of outer space as heat sink. Hence, energy can not accumulate at all unless either thermal absorption or radiation changes.

I would agree with you when you say that: "The atmosphere is in dynamic equilibrium with the Sun as primary heat source." If you would indicate that this condition was prevalent before the so called "nuclear age."
You see, today we are digging into those "tiny amounts of geothermal heat" and we are spreading that "heat" into the atmosphere. (As I understand it, the "geothermal heat" is caused to a large extent by the radioactive materials inside the earth.)

We seem to be talking different languages when it comes to these ideas.
You consider "the cold of outer space as heat sink", I have always considered a "heat sink" as a device that conducts heat away from some hotter object, space can not "conduct" heat away from anything.
As far as I know there are only two ways in which outer space can cool an object, one is through the loss of radiated energy and the other is the loss of the hot molecules into space.

You say that:

energy can not accumulate at all unless either thermal absorption or radiation changes.

If we irradiate the atmosphere by spreading radiation in the form of radioactive atoms into it, then I believe that the "energy" of the air molecules will increase and accumulate, unless the irradiated molecules re-radiate that energy into space or the molecules themselves escape into space.
Before the "nuclear age" our planet was in thermal balance between the sun's energy and the re-radiated energy from the Earth, but now we are slowly increasing the "motion" of the air molecules by introducing radioactive molecules into the atmosphere.
IF the atmospheric molecules increase their motion, (kinetic energy) then the atmosphere will expand towards space, seems like simple laws of physics to me.

You said:

The total pressure exerted by the atmosphere is quite small compared to gravitational pressure from overlying rock strata. No significant expansion is therefore possible even if the entire atmosphere were to vanish.

Do you have any proof of your assertions?
What is the total weight of the Earth's atmosphere?
What is the total pressure inside the Earth?
It seems to me that these "pressures" are in equilibrium, except in areas such as volcanoes where the lava can be "spewed" high into the air, or even "pushed" into water that is deep in the oceans.
Similarly, it seems to me that the fault lines are weaker points in the planets surface that would be more sensitive to pressure differences.

You said:

Heat from nuclear waste products is trivial compared even to geothermal heat, which is in turn trivial compared to the Sun's input. Forget it completely.

There is much more than "heat" being generated in a nuclear disintegration, it is only when the nuclear "fragments" accelerate the surrounding molecules that "heat" is detected.
How is all the other energy, such as gamma rays, dissipated, and what actually happens to the alpha and beta particles when they are released from their original nuclei?

You seem to be advocating that everyone "forget" that hundreds of lakes have disappeared, that many other lakes have very low water levels, that the glaciers are disappearing, that Earth's surface temperature is increasing, that high altitude temperatures are becoming colder, that there are more hurricanes and typhoons, that there are greater number of earthquakes, that the temperature change between night and day is greater, that the sun's rays burn peoples skin much quicker, that more people develop cataracts because of the increase in the intensity of the sun's rays, that the ozone layer is disappearing from around the planet, that all kinds of other problems can be attributed to the possible increase of "kinetic energy" of the atmospheric molecules.

Why is it that no one should investigate the possibility that the cause is radioactivity?

You said:

Average atmospheric pressure has not changed by so much as .01 % in the past century. Hence, no such effect is possible.

We have not been spewing radioactive contaminants into the atmosphere for a century, so that argument is invalid.

You said:

Hence, your post is scientifically incorrect. You are presuming effects many orders of magnitude larger than the causes that you cite can produce.

I suppose that you have the answers to all the observed changes that are taking place around the world, if so, then why not tell us about it.