I would absolutely water less than once a week. Maybe once a month in the winter, especially with that soil. With that being said, not sure what the spots are from, sorry. I had a similar looking spot that resembled a callous from a cut on a leaf on my blue chalk stick so I just cut it off.

Sans, what?! You mean paint can't make babies and spread all over the Op's plant? I'm just throwin out possibilities:). Could be scale. I've been fortunate enough to never have it, but I know they come in all shapes and sizes. With scale I would think it would feel like something when you rubbed your finger over them. You say they feel like nothing. My other guess would be mineral buildup. If this was mine I would take it out of the pot and inspect it. Roots and all. I would get some rubbing alcohol and wipe down every leaf with a paper towel or q-tip. Clean the pot real good, and put in new soil. Throw out old mix it was in. To me it doesn't look like a pest, but I'm not there I can't feel it or really inspect it. It's hard to tell in the pic:). Keep this plant away from other plants:).

Mechanical damage and potentially slight over watering? The depression could be fungal.

First, don't do any treatments until you know for sure what it is. Fungal disease should be treated with a fungicide. I had some fungal disease on one of my aloes and treated it with powdered cinnamon (natural fungicide). I wasn't 100% sure what it was, and couldn't get ID here either. What I did helped. I didn't isolate plant and it didn't spread on other plants either. It may depend on what disease it is exactly - I am not sure. Rot usually spreads thru the plant, not really on other plants unless in same pot. It usually happens with overwatering, and culprit may be/often is water retaining soil. Depending how bad it is, it may be good to cut off infected parts, repot, check the roots...