no bare wire or lug should be touching the coin mech frame or the coin mech when it's installed. Check places marked with red arrows below.
since you don't have the coin lockout armature, there's no point in connecting the loose wire to the coil. You should tape off the end (pull it out of the grommet and tape it outside the mech), and make sure the bare coil lug isn't bent up/down enough to touch the mech or frame.
the metal parts of the game are connected to the mains ground ... they shouldn't be connected to any of the 6V or 50V circuits. Reading voltage with one probe on the metal parts should give a misleading answer.
if you are measuring ohms (power off) from a circuit to the chassis metal parts, you should get a reading over 10 megohms. If you get a low reading of a few ohms, then something is shorted to the metal. If only one thing is shorted to metal, the game may work ok, but you have a current path that is connecting something in the 6V/50V circuits to mains ground (and eventually neutral back at the circuit panel) in the 120V circuit. That can result in flaky behavior.