Only six of the above respondents mentioned structure/structural integrity of the house!
An inspection would likely pick up problems. But why spend money if you can see the obvious yourself?
My five:
*Location, location, location.
*NEIGHBOURS. (Yes, I AM shouting!) Any neighbouring property with barking dogs, overgrown shrubbery, inoperative cars in the driveway, wind chimes or weeds gets my thumbs down. I can never forget a business colleague who bought his first home attached to a "halfway" house. Interesting crowd hanging out there at all hours of the day and night.
*Structural integrity. Only put it third as I tend to demolish most homes I've bought.
Q