Drop targets aren't too bad to work with, really.
Here's what I'd do, if it were in my shop:
I'd take the whole target assy out. Should be easy as the only thing that solders in is the solenoid - the PCB with the switches should have 2 connectors, one which goes to the switch matrix, the other provides power to the drop target PCB.
Take a good look at which wire connects to the banded side of the diode, and which wire connects to the unbanded side of the diode. Taking a picture isn't a bad idea. It is important that you reconnect the wires to the correct tabs, otherwise you could fry the diode and the driving transistor.
Next, move the entire unit to a workbench or table. If it's your wife/girlfriend/significant other's kitchen table, be sure to put down a good towel or two to make sure you don't scratch anything up.
Take notes as to where everything goes in the assembly. There are E-Clips, washers, springs, etc. The order these go in is crucial, put them out of place, it just won't work right.
Take the whole works apart, and clean everything real well. I use a citrus degreaser from the local dollar stores by the case, 'LA's Totally Awesome Orange' - it's a buck for a 22 oz bottle. I buy it by the case as I said. It's good for most everything. I would use this on everything *but* the PCB!
You'll want to spray everything liberally down, and use a medium to stiff bristled brush to scrub everything. An old toothbrush will work, a brush with slightly stiffer bristles will work better. You don't want a wire brush, and a paintbrush will probably be too weak.
If you have sensitive to dry skin, you'll want a pair of gloves while you do this. The citrus degreaser has alcohol in it, and dries your hands out.
A new coil sleeve would be nice, but is not required for a drop target assembly. Well, it *is* required in my shop, but I'm picky. You can use a bottle brush, or even a paper towel or rag sprayed with the degreaser inside the sleeve and it'll clean it pretty well. I always replace them, so it's not a concern in my shop.
You could tumble all the metal bits after cleaning them, but it's not a requirement if you don't have a tumbler. All that's going to do is make them a little extra shiny.
For the PCB, rinse it in hot water, then spray both sides down with scrubbing bubbles. Yes, the bathroom cleaner, you read that right! Take a paintbrush and rub the scrubbing bubbles in. If the board isn't clean, do it again!
Rinse it well, rinse both sides with 91% alcohol or better, and let it dry. If you have an air compressor, you can dry the board that way, but I'd stay away from the optos with the compressor.
Let the board dry at least overnight. If you can, put it on a piece of cardboard and stick it out in the sun for the day. Flip it mid day. That'll get it good and dry
*then* reflow the solder points on the board where both connectors attach. Cold solder joints on these boards are not uncommon.
Reassemble and test, I bet it works a ton better afterwards.
Having said all of that..
If you don't want to go to that level of detail, that's fine. I'm sick in the head, and you may not be 
Start by reflowing the connectors on the opto board, and cleaning the optos with a q-tip sprayed with windex.
Somers, NY
Guelph, ON
