Put your face by the headstock and look straight down the fretboard as though you were using the strings as a gunsight. Does the fretboard appear to be warped even slightly, or does everything look dead straight?
Look at the side of the neck. Use one hand to press one of the strings down against the first fret, and use the other to press the same string down against the last fret. The string will be a straight line, but how bowed is the fretboard? How much space is there between the string and the 10th or 12th fret? A little bow (a couple mm space at the 12th fret) is normal, but if it is more than that, or if it is not bowed at all (string touching the 12th fret), then you want to ask questions about the truss rod. If you're at a shop, ask if they can or will adjust it. If you're at some geezer's house, ask if they ever adjusted the truss rod, or if they know of any issues with it. If they say something like "I tried to tighten it, but the nut won't turn" or "the nut just turns freely, doesn't seem to do anything" then be suspicious of a damaged trussrod.
Are there any gaps or cracks between the fretboard and the neck?
Are there any cracks (even the famous "hairline crack, very stable") in the headstock? A crack in the headstock can be anything from no big deal to a total disaster. Check especially for cracks around the tuning machines.
Plug it in. How does it sound? Turn the knobs a bunch and see if they crackle or are intermittant. Generally speaking, if they crackle just a little, they can be cleaned up; but if they crackle badly/harshly, they may need replacing. Solo each pickup (switch or vol. knob full on for one, full off for the other). Does each pickup work, sound good, and work across all of the strings? If there are no strings, you can use a small screwdriver or pocketknife to tap the pole pieces of the pickups to hear if they are working.
If you have the opportunity, open up the control cavity. Is there any rust, loose flying wires, obvious repair jobs, gobs of electrical tape, etc.?
That much will get you a long way I think.