I have a 4-plex, C property, 2/1, built in mid 60's on a slab with very little insulation. 

I always highly recommend removing any lead pipes in a home or building and replacing with PEX or copper.As far as asbestos which is usually insulating pipes or old duct work ( very rarely have I seen it in walls or in attics for insulation) I usually just leave it alone and not disturb it unless being told by someone to at which point I take the same steps as I do with lead

Insulate and drywall.

Good idea to be proactive as well...install pipe insulation, seal cracks, install electrical heat tape to pipes, etc. 

There is asbestos insulation, and rotten sills on both the garage and the main house, and electrical problems (short in the bathroom, no grounds, and not enough AMPS for the house).

Weather stripping Doors (rear house door) – better seals, light and air getting into building Glass in same door is cloudy – thermal insulated seal failure Back Decking: The deck band adjacent to the deck steps has cracked, which is causing the deck to exhibit signs of sagging andfailure of the floor structure, which could result in deck collapse.

Asbestos can cause health problems if it is inhaled, so if you have any exposed pipes that are insulated with asbestos you should replace the insulation, however it is unlikely even that would cause a health problem.

Positives of the House: Amazing updated high end kitchen all stainless steel appliancesNew RoofCan lighting in all bedrooms, living room, and kitchenHigh End basement bathroom includes Jets in shower wall and Heated tile floorNew Central ACNew FurnaceNew HVAC ducting throughoutNewer Vinyl SidingNewer guttersMany newer vinyl windowsNewly wired for gigabit speed ethernet in all roomsOpen cell insulation on second floor roof (solves all cape cod style home problems with ice damming)Nice landscaping both in front and in backGreat curb appealFenced in LotFull BasementOpen concept living roomVery low taxes compared to rest of Lake County IllinoisFinished will have 2 full baths, 3 bedroomsNew copper plumbingNew Natural Gas pipingAll Capital Expenditures are taken care of!

Another solution may be to vent the attic space, if it is getting to hot up there and cool downstairs, that will cause humidity at the ceiling and  while your at it check the insulation in the attic, make sure there is enough to keep the temperature difference between the cooled space and the hot attic. hope one of these helps you.

Is the slab insulated (underneath) and heated (hydronic or electric in-floor)?