It's not so much the age of the house that would concern me (I actually like older homes), but the condition of it.
Things I would check for are: a solid foundation with no crumbling, major cracks or shifting, square outer frame and straight inner walls, floors that don't slope (put a marble down in the center of any suspect rooms and see if it rolls, assuming no carpeting) and no water damaged ceilings. That's for the general structural condition of the house.
Further, ask about/look at electrical. Obviously knob and tube wiring is a no go, although I doubt you will find that anymore, even on the oldest houses because companies will not insure such a house. However, aluminum wiring was used on houses around the 60's/70's I believe, so open up a switch plate and take a look. That wouldn't freak me out though because it can be pretty easily replaced with copper - it's the junction points that are critical, not the whole house. While you're there, see if you can see the insulation in the wall. If it's fibreglass, you're fine. You can also look in the attic to see what's there. When I bought my house, I had the sellers confirm that there was no asbestos as a condition of sale. Asbestos floor tiles or ceiling panels in themselves are not a danger unless you plan to remove them, then you need to get a qualified professional to do it.
Depending on where you live, mold may be more or less likely. I'm allergic to mold and get very sick from it, so this would be a bigger issue for me than anything else. But I also have a hound's nose for it, and any significant amount is readily detected. Just look closely at walls and baseboards, check windows and ceilings for leaks or obvious musty smells. And of course, any rotting woodwork is a red flag.
So depending on how much I liked the house, location etc, any one of these things wouldn't necessarily put me off. A combination of them that meant a lot of remedial work might, but if the seller is willing to drop the price accordingly, then it still might not be a deal breaker. If you can take someone experienced in home construction to look at houses with you, then do so. Or just get out there and look at lots of houses on your own so you get some practice at it.