Is New York City soot NYC noise detrimental to my houseplants? Will yhe soot harm my plants which are sitting on a sill? Is it harmful to wipe down the leaves of my aloe and jade plants with a moist cloth? (My other plants are cacti)
Lastly, will the constant hum of an air conditioner just outside my window damage my plants?: In effect, drive them crazy.

Actually believe it or not smog is benificial to house plants, as they love to eat up the CO2 in the air. It is when they are outside and basically get a sugar rush from pollution ( acid rain ) at the wrong time of the year this can do some damage to them. Wiping off the soot from the leaves is a good practice. just becareful not to be rough enough to injure the plant.

I just read the second part of your question.
The noise won't bother them but the draft from the AC may. Plants don't have ears or brains, so the noise can't bother them, but plants do respond to music however. My theory is that the subtle vibrations loosen the soil around the plant and stimulate root growth. but that is only a guess on my part.

As a fellow New Yorker, I am all too familiar with the soot that seeps into all of our windows. I am not as conscientious as I should be in cleaning my plants, but they have not suffered. (My lungs may be another story!)

If the dust is allowed to accumulate too much it will reduce the amount of light available to the plant. This reduction in light is not good for the overall health of your plant.

No need to be obsessed, but it is definitely a good idea to wipe the leaves periodically with a damp cloth. It will also make them look healthier.

No need to worry about the AC, as long as it is not blowing directly on your plants from close range.