Yes…awesome andrew! In short, everything mentioned above. Bring a flashlight to shine through door jambs (closed to find warpage), and here’s a cool one-marbles. You can set the marbles on the floor (esp. if they’re hardwood or hard) to check level and to see if the foundation is tilting / leaning anywhere in any rooms.
-Mold: Another one to check for is mold-smell test, but also look in dark areas especially ones connected to outer walls or if the walls are shared with lawn/ground floor-as water may be collecting from the outside in…little black dots are a telltale sign that there may be seepage there.
-Water pressure, noises in the pipes; make sure that if you have a lawn that you fire up the sprinklers; in my house (built in 1904!) in the early morning hours when our sprinklers come on, the pipes shudder (usually a sign of old pipes and a warning sign).
-Electrical: check service panel to see what kind of fuses and total amperage the unit is set up for; if an older unit, the panel may be on the low side (less than 100 amps)...if major appliances are hooked up to these circuits, it could be problematic. You can do a quick check by switching on all the lights in all the rooms and having one person turn off circuits one at a time to see what goes on/off and see what’s on each circuit. All major appliance outlets should be terminated with ground plugs (3 pronged outlets); if possible, un
-Check the roof, and should not have more than two layers of roof tiling (if its shingles), otherwise, if it has ceramic/clay tiling, check visual inspection. Inside, check ceiling for water spots, or other ‘new’ popcorn ceiling installations (usually added to cover up stains from water leakage).
-Check walls for evidence of cracks (could be a sign of shifting / cracked foundation if severe enough).
-If at all possible, check drainage of sinks in kitchen and bath; slow drains can be a symptom of a deeper clog down drain (past the trap).
-Termite damage: small pencil-lead-sized holes, or any buildup of what looks like sand granules are evidence of termite ‘poop’ and live infestation. As part of the process, a recent termite inspection should be verified (within the last 5 years), and if it hasn’t, should be performed prior to close of escrow, and at the cost of the seller.
-Some other more obvious checks: Windows all open/close, doors/locks all work and open/close; main access doors don’t shake when closing; If an old house, the issue of whether or not it has been retrofitted for earthquake will have an effect on the selling price, and most certainly on your ability to qualify for full coverage insurance vs. California Fair Plan (what I have since my house is very old).
You may also want to contact an insurance broker soon, to get opinions on coverages for the unit based on condition and age of the building, its electrical, plumbing, foundation, etc.
Best of luck!