Wow, thanks for this. I'll be sure to use your advice , probably one of the most comprehensive guides I've seen.I mention these points, because I've been caught out on them myself.
First, don't listen to any "Oh, it's just got a flat battery" excuses: if it isn't functioning, battery or not, walk away -or bring a battery with you.
Second, also bring a cheap film of any kind (to try out the auto-load, advance, shutter at all speeds- and rewind mechanisms). I have had various cameras showing the following faults after I paid good money and brought them home: mirror in lock-up (nothing would function, because the mirror stayed up and wouldn't respond to the re-set procedure; a clip was broken off (and removed from) the film compartment, thus disabling the auto film loading mechanism; the advance mechanism refusing to work after several exposures and going directly into the rewind mode; skipping frames, because the advance/shutter interlock worked only intermittently at best; the shutter freezing after a few shots, or refusing to operate at all at the slower settings (1/15th sec and slower).
While loaded with your film, check the operation of the auto focus (if any) and the clarity (specks, mould) of the viewfinder. If on a clear day, between 10 am and 3 pm, point the camera at the the blue sky away from the sun (or onto green grass, with the sun behind you): it should indicate an exposure (equivalent) in the vicinity of f/16 at 1/film speed (ISO) +/- a stop.
Remove the lens (with SLRs) and check the condition of the lens (look for spider-web like growths or mould-like splodges. If you see any, walk away. Also, check front and rear elements for scratches, grazes, smudges, chips. If the marks appear to be permanent, walk away. Make sure the lens is clean before you start looking (bring a lens cloth with you and ask for permission to clean the lens first). A grubby front and/or rear element can obscure many faults. make sure you have good light (bring a flash-light with you).
With the lens removed, look inside the miror box. Inspect the mirror for damage and smudges. The mirroring is on the facing side of the mirror and very vulnerable. If damaged, you don't need it. Sometimes, however, there may be a strip along the bottom of the mirror where the mirroring has worn away due to contact with the (rubber) mirror buffer: this may still be OK, providing it doesn't show through the viewfinder. Check inside for cleanliness and lack of damage.
Open the film compartment: check for the condition of the (rubber compound) light seals. Are they tacky, crumbly, falling apart, smudging your fingers? If so, they can be replaced, but....? Check to see there are no rough edges on the film-path/film guides and (especially) the pressure plate. Check the condition/operation of the film compartment door latch. Is the door itself buckled in any way?
Run the shutter at all speeds and view the action of the shutter blinds: you should notice less and less light passing through the shutter as you increase the shutter speed. Do the shutter blinds look clean, unmarked, without any holes in them, and not buckled in any way?
With fixed-lens cameras, does the shutter operate at all speeds and does the iris diaphragm close right down to the set value before the shutter operates (no "sticking" diaphragm blades)? With range-finder cameras, the rangefinder mechanism itself may either be out of adjustment or the optics obscured with mould. This is often expensive to cure even where possible. Rangefinder "between the lens" shutters are notoriously difficult to service (if you can find anyone at all willing to do them in the first place).
look at the outside of the camera for "dings", dents, scratches, worn away coatings, etc. has it been dropped? You may be willing to accept some "battle scars" for a reduction in price, but there are many near mint copies out there so again....?
Pick up the lens(es). Try rotating the aperture or zoom rings (if any). Is the action smooth?
is anything wobbly or rattly? When the lens is mounted to the camera, the lens-camera combination shouldn't rattle. Is the rubber grip in good condition? Look through the lens from both ends: is anything lurking in there that shoudn't be? Sometimes internal lens-elements will undergo partial separation: this looks a bit like oil-film slick (with a light diffraction pattern) on water. Try all the levers you can see for action; does the diaphragm open and close easily and smoothly. Is the iris regular or distorted in shape?
When examining the lens, use a flashlight and shine it in from the end opposite to the one you're looking in. A flashight will reveal much more than any other -including daylight.
(One seller, with mould in the lens, had the bright idea of using a 25 watt bulb in his garage (at night) for me to view the lens. Luckily, for me, I was still able to see the luxuriant growth of mould filling the inside of the lens in question.)
Run through your entire practice film, taking shots around the seller's (indoors and out) -so as to actuate any auto rewind mechanism, checking all the while whether the displays are functioning, including the frame counter- and if you don't notice anything suspicious, you have agood chance of everything being OK.
Take your time and refuse to be hurried: it's your money!
If you do notice anything suspicious or worrying, walk away now: it will be much less trouble and expense to wait for a better opportunity than to try to fix a bad bet.