Oh, I meant wash the whole damn thing.
It definitely comes apart from the back. The coin mechs all come off and finally the reject mechs do.
Page 38 and 39 show a blown up view, but if you look carefully you'll see that a few nuts come off and the whole back comes off, then it's just a matter of pulling the reject buttons out.
http://www.arcade-museum.com/manuals-videogames/A/Asteroids.pdf
Take A LOT of pictures or film it and walk through talking about everything you see: "These are the wires from the harness. They attach here and here and here with zip ties. Look at these little bolts, there are seven, they don't have washers." You'll feel a bit silly but will thank yourself later. Sometimes it's weeks until you put it back together and you will forget.
These types of things are invaluable in repairing and then putting back together. Bag all hardware together in baggies and label the bag, like coin door. If you film it well beforehand you'll be able to see the various screws and bolts and where they go. A coindoor is a great jumping off point.
S.