When they say "it leaks" was it a drip or a constant stream?   Finding the source of a leak is a lot easier if you can observe the washer  in operation but you probably won't have that luxury.  You'll have to go through the machine from where the water line connects to the fill valve and follow the water path every step of the way until you get to the drain hose.  I would look for loose connections first and then look at things like a gunked up float that's allowing the tub to overfill or a gasket that might be failing.  User error shouldn't be overlooked either.  I can imagine a blocked wash arm spraying water continuously at one spot on the door edge might cause some water to escape eventually. 

I'm working on a KD12 right now and found a couple iffy gaskets.  At least you stand a far better chance of finding parts for an 80's model than I have for one from the 50's!