Heather: "...For example, I thought the distant mountains (in my photo) looked too washed out so I was going to try and do something to perhaps darken them (contrast or shadows?..."
Atmospheric haze between you and the distant mountains is what is causing the loss of contrast. Leaving it in, is more realistic - no question about it.
In fact, in the old days, people didn't like it either, and its effects were reduced by using a glass polarizing filter in front of the camera lens. These days, one can do more or less the same thing in PS. I would regard a change like that as a creative decision, not a purely technical one. Compared to the major negative changes that can be inadvertently introduced by a bad monitor, this is a relatively small, safe tweak.
Probably the easiest way to move the image in this direction is to bring it into ACR and:
a) move the "clarity" slider to the right by a couple of points;
b) move the contrast slider to the right slightly; and,
c) go into the HSL/grayscale tab, and slightly increase the saturation of the blues, and slightly decrease their luminosity.
Now, to come clean ...
... I felt exactly the same way as you about it, and if you look carefully at the image I posted yesterday with the arrows, and compare it to your original, you'll see that I couldn't resist the call of saturated colors and already made the changes I just described to get a more vibrant look.
Great minds think alike -- Ya caught me!!!

Tom