Can't make a general call on this. Case by case (so to speak
If yr casings are painted, then minor dings can be filled with any spackle. Use a small <2" putty knife to be able to work the contour/reveals well. A new coat of paint, and yr good to go. I'd probably NOT use dwall compound. That might shrink and prob can't take new nicks/gauges as well.
I'd definitely try to do it this way b4 considering the alternative: replacing the whole case. That's mitering/nailing/caulking. I'd only do that on the ones that are severely gauged.
Of course, replaing the casings around windows is a good opportunity to get in there with some weatherproofing caulk...