[Fr. Frank]

Check the floor by walking every inch of it on tiptoes and kind of bouncing as you go. If there are any significant soft spots, you'll probably be able to feel them flex under your feet. With the motor at slightly tilted up, put a rod through the fixed tilt angle hole on the transom bracket, and lower the engine down until it contacts the rod going through from side to side. Now stand on the lower unit cavitation plate, and again, bounce up and down. Look for any signs of flexing in the transom as you do so. (Putting the rod through takes the weight off the hydraulics)

Pull all the spark plugs and examine them for color and deposited carbon. With all the plugs out, run a simple compression test on every cylinder. Compression on an '83 Merc 200 should be 100 - 140 lbs per cylinder, and no more than a 10% differential from highest to lowest reading.

Unfortunately, a big carb'd Merc that hasn't been run in a while will undoubtedly need the carburetor cleaned out. The fuel jets are notorious for accumulating gum or varnish in just a few weeks of sitting. Often the motor will run, but will idle on only 4 or 5 cylinders, or idle okay, but develop reduced power because of clogged main jets. You can run Quicksilver PowerTune through the fuel lines with the fuel if you can find a bulk dealer in PowerTune. (I used to buy it by the gallon, but that dealer no longer sells Mercury/Quicksilver prodcts or outboards)
Fastest way is simply pull the carbs and perform a cleaning. Doing all 3 carbs takes under an hour, including re installation.
Look for signs of decaying wire insulation under the cowling. Aftermarket replacement wiring harnesses are available if necessary.
Check the manual for alternator specs, and then check alt. output. ( I believe the early 80's V6 Mercs were either 6 amp, 10 amp, or 18 amp output. 6amp if you have the black stator, and 10 if you have the "green" stator, and 18 amps if you have the "red" stator. I also confess that I have no idea what those color designations describe. I know my '92 150 has a 6 amp alternator, though)

At any rate, check these things.