FYI, water cooled mowers is a quite old. Honda mowers got all of those checks too, liquid cooled, oil pump + filter, twin cylinder, rubber engine mounts, shaft drive with a true gear to gear transmission but shifts like a hydro-static.
Not much goes wrong with these, deck rusts out after 20+ years of use if not cleaned ever, pto clutch + break generally is the first clutch to go and the second clutch, the drive clutch is the other wearable item. Change the belt every like 15-20 years and keep the fluids in check. Not sure if it's true, but I read that JD assisted with the design with Honda so probably why the two are similar.
Btw, did I say this was a mid to late 80's lawn mower? They also made some models in the 90's.