Asbestos flooring, drywall, insulation, etc. If disturbed, during remodeling for example, asbestos can be an extreme health hazard.
Old plumbing/sewer lines and electrical wiring. These can leach lead into your drinking water, cause raw sewage to back up into your home which is destructive and a health hazard, present fire hazards, and all are very expensive to replace.
Foundations that lack French drains and proper landscaping around the foundation walls. Improper water drainage is the number one reason older homes develop structural problems.