I'm going through a remodel on my grandpas old house that was built in 1950. Overall the base structure was in good shape and there were only a couple issues from the initial build (they didn't stagger the seams on the center laminated beam). They built the older houses to last compared to alot of the new ones. By the time its all said and done with remodeling/updating and fixing stuff on the house I'll be at $80-100k.
As others have said
- Asbestos test for linoleum & hvac insulation
- Plumbing condition (ability for all the fixtures to drain quickly) Also check the soil stack to make sure its not plugged (my south one was 100% plugged).
- Electrical. All of the wiring in my house was woven fabric insulation over aluminum wire. As soon as you moved the wires to even remove an outlet all the insulation would fall off (brittle). I replaced every piece of existing wiring with new romex because of this. Also if it has a glass fuses look into changing to a breaker box. Also inspect to see what all is on which circuit. In houses of that era they tended to daisy chain huge parts of the house together, and its usually random what they hooked up. The electrical side can be a huge cluster and for me it was WAY faster and easier to junk the whole thing and start over.
- Windows. Find out what is in there for windows and look for any damage around/under them. My grandpa bought the cheapest double pane windows he could and got a really crappy installer. There is alot of damage under most of the windows that I had to cut out and replace because it was completely gone. To top it off the installer just used silicone to install the windows
- Siding/Roof. Obvious stuff here. If you have to replace them don't cut corners. All the houses I've had in town had pretty old roofs and they would last. Out in the country they only seem to last 10-15 years. My next roof will be metal Decra or similar.
- Septic. Depending on where you are the rules are different. Here if the house changes hands to a non direct relative the septic must be updated. You have to have a properly sized dual compartment tank and a leech field. These can easily cost you $15k or more and around here can be deal breakers. In some cases the septic is in a place where you can't conform to the new rules so you have to move it which is even more $$$.
- Well. As was said make sure its decent and see what the quality of the water is. Also find out how deep it is since that can make fixing the pump more expensive. My dad lives 1/2 mile to the south and his well is 40-50ft deep. My place the well is over 150ft.
- Internet. Depending where you are you may not be able to get anything. My dads place is right at the very end of the line for high speed and its barely even DSL speed. My place 1/2 mile to the north is just too far to reach so my only option for now is to run satellite or a radio broadcast service they have here and neither are cheap. The kicker is they are running fiber along the highway in front of dads place to town and we can't tap into it. I'm hoping in the future we can get that service. Streaming movies is 100% out of the question.
Overall nothing was really show stoppers but the original budget was $60k, but as with almost every remodel on older houses every time you open something up you will get smacked with some kind of surprise. The electrical, windows, and associated rot were not planned for at the start. Nothing was really a knock the house down and start over issue, though if some of the issues were not taken care of after a few years it could have gotten close to that point.