The dry firing will do quite a bit, plus can make some stuff show up.
I am not a trained S&W smith, but here is the basic job. Check for end shake and timing first. If those are good, remove side plate, look at side plate and showing side of, hammer, trigger and trigger return slide. Any shiny spots on those are probably coming from hish spots on side plate. Use small die makers stones to polish high spots and the "buching" area where hammer and trigger studs go. Not trying to take anything down except any little burrs, mostly just a little polish. Remove trigger return slide, trigger and hammer, Do the same thing to inside of frame. Be sure to check bottom of slide and where it rides on frame. Install 13# tension Wolf trigger return spring on re assembly. If the side of the hammer or trigger has been dragging on the frame (arc mark on side of hammer or trigger stick a hammer stud shim on the drag side. Reassemble with factory main spring, But leave tension screw 3 complet turns lose. Have a bunch of CCI primed cases, NO BULLET NO POWDER. Fill up the chambers with these pieces of brass. Pull dbl action trigger. Doesn't fire? turn screw in 1/2 turn, and try again, doesn't fire? another 1/2 turn. Once it fires. First the trigger might get bad because the primer may back out some and having no recoil to slam it against recoil shield it will drag. Open cylinder and fill with fresh primed cases. Does it fire on every chamber (keep removing fired cases that drag. You can avoid this primer dragging by drilling out the flash hole in primer pockets to about dbl their normal size, but make sure they NEVER get used for live rounds. Anyway get it so it fires every primer ever time. Now tighten it up being careful to count turns 1/2 turns, 1/4 turns. Remove screw and carefully measure with good calipers. Shorten by .0078 for every 1/4 turn. Say 1 3/4 turns + 7 1/4 turns so .0054 needs removed. But always leave a little long. slightly round tip as you do this. Reinstall tighten and go shoot it. PS Smooth and reliable beats light and not reliable.
Years ago in the seach for the perfect trigger I took a model 28 and put a dap of fine polishing compound on studs, pivot points, sear surfaces etc and the dry fired it a bunch and then cleaned everything back up real well. I couldn't notice much improvement.