For us, it would be major foundation problems; major leaks (roof or plumbing), especially if they’ve been active leaks over a long period of time; or major structural issues.
Also, certain types of easement or land use issues could be deal-breakers. A new development going up nearby that would significantly affect the property and quality of life there could derail the deal, too.
That being said, you can negotiate your way to a good deal with these issues. If you can cover the total cost of repairing these issues using very high-quality materials and contractors, plus get something for your time and trouble, then it could be a good deal.