A 1970s house is right at the age where you'll see both original systems still hanging on and the first wave of replacements - some done right, some not. The foundation, roof, electrical and plumbing are absolutely critical, and I won't rehash that since others nailed it. But here's what gets overlooked: **insulation and ventilation in the attic**. A lot of older homes had insulation standards that are laughably inadequate by today's codes, and poor attic ventilation can cause roof rot, mold, and ice damming in winter. Have the inspector actually get into the attic and look at how it's vented, not just glance from the access hole. Also check whether any previous owner tried DIY electrical work or plumbing patches - unpermitted work can mean you're inheriting someone else's mistakes, and it becomes your liability.
The other thing people miss is the condition of windows and doors, especially in a 1970s place where single-pane glass is common. You're not looking at immediate catastrophe, but thermal efficiency is genuinely expensive to fix later if you care about heating bills. Same with any visible water damage - even small stains on ceilings or drywall can indicate a roof leak or plumbing issue that's been intermittent, and those are harder to diagnose than a fresh leak.
Get a separate termite and radon inspection if you're in an area where those matter. The radon test especially takes time and you want the results before closing. And if the inspection reveals major issues with those big systems, you're in negotiation territory - don't assume you have to walk away just because the foundation needs work. Have a contractor give you a ballpark on repairs. What sounds like a dealbreaker might be manageable, or it might be the leverage you need to renegotiate the price.