If the roof is the original from the 1980's, water damage is more likely to either have already happened or will happen if the roof has not been maintained or replaced. Water damage can sometimes occur where the damage isn't visible, like behind wall boards. Ignored termites can also become a problem since the soften wood will attract them. Plastic water pipes should be checked for leaks or replaced since they are likely to cause leaks at the connections compared to other types of pipes. Mold can also form water damage in unseen areas, which can weaken the house structure and cause a possible health hazard.
Up until the mid 1980's the copper pipes in the houses built did have some traces of lead, which can be fixed by installing filters on the water pipes or replacing all the pipes entirely. Before repainting or removing paint, see if the paint is lead based. While lead-based paint became illegal in 1978, not all paints already produced were destroyed. Some 1980's homes have tested positive for lead-based paint, some built as late as 1987 -- nine years after lead-based paint was banned. Test both interior and exterior paint on the house. If the paint tests positive, there is a chance that some of the paint may have contaminated the soil around the house.
Homes built in the early 1980's are more likely to have traces of asbestos, but finding traces of asbestos in newer homes is not entirely uncommon. Asbestos is difficult to detect since it gives no odor and cannot be seen, so a professional is usually needed to take samples in the house. Some cities will require renovation to stop, and permits are often needed to make sure that the asbestos is properly disposed of if found. Asbestos can especially become a problem if walls are torn down or floors replaced. The fine dust can become airborne, possibly causing health problems.
Common in the 1980s was for a builder to install horizontal furnaces in the attic. These should be promptly removed and replaced. They were recalled for becoming a potential fire hazard but not all were taken out of homes. The recall was because the NOx rods would become brittle and could fall to the bottom of the furnace, possibly setting the house on fire. If the house contains a horizontal furnace, this should be the first appliance to be upgraded because of the potential fire hazard.