>>2860856Shutter curtains should look absolutely pristine, there are two sets of curtains and both should be good. Open the back and flip up the mirror to see the front and back, cock the shutter to see the first set and then release the shutter to see the second set. If there's and creasing or it looks like someone tried to shove a finger through the shutter then just walk away immediately.
Check the black foam light seals which go all the way around the film door. Over time the foam gets old and crumbly and falls out, which causes light leaks. It's a pretty easy DIY fix to replace the seals with new foam, but it would of course be preferable if it was in good shape to begin with. There should also be a foam cushion at the top of the mirror box where the mirror flips up. If it's rotten you'll probably see lots of black chunks in the viewfinder, it has no effect on the photos but it's annoying and you have to clean it.
Check the battery port for any corrosion from leaking batteries. Then put a fresh battery in and see if the metering lights in the finder light up and if the meter seems to work correctly.
Fire the shutter several times, going through all the speeds. Nothing should sound weird, look through the curtains as the shutter is firing. See if the mirror flips up and down properly and put a lens on the camera and see if the aperture stops down when you shoot. Listen to the slow shutter speeds, each one should sound twice as slow.
Check the serial number to see if it's an FM2 or an FM2n. They're identical externally and are functionally pretty much the same, but it's good to know. The serial number of an FM2n will start with N.
The FM2 is an excellent and legendarily reliable camera from back in the day when Nikon made the toughest cameras. This was the model that most pros kept in their bags as a backup. If the one you're looking at hasn't been obviously mistreated, then it probably won't ever let you down or give you up or run around and desert you.