Ignition/key switch problem?

I have an 82 SN 2001. Motor runs great. Put a new ARCO starter on because old one was dragging. Cranked in the yard fine on hose. Took out next day, fired right up, left landing and at about 20 MPH had the slightes miss in RPMS. I mean I looked at my son and said "did you notice that?" He said "barely".
     We proceeded to cruise on down the lake at 30ish MPH. About a mile from landing the boat just died! I mean like the switch was cut off! We coasted to a stop. Motor would not turn over at all with key switch. So opened cover, and all I had was a Philips screwdriver. Took off solenoid cover, and with key switch in on position, arced across solenoid posts and motor fired right up. We decided to ski the course close to our dock and ran motor for 4 hours with no starting problems whatsoever. The only other thing I noticed was sometime when the key was turned into the start position, the motor would turn and turn and would not fire until it was switched back to the run position. I tried checking with meter but it wouldn't do it to save my life in the yard. Would it be correct to assume this problem is in the key switch or somewhere else? Thanks