Go to
www.PinRepair.com and read their guides on repairing that 90's williams stuff. You'll find all the info you need there.
Basically if the flipper is sticking up, it's one of two things, either a. the game is 'holding' it up electrically, or b. it's just getting stuck, mechanically. the first thing you need to do is figure out which of the two it's doing.
If you open the coin door, they'll be a lever that releases the lockdown bar above the coin door. Pull it off, then carefully slide the glass towards you and out of the machine. Close the door back (to turn the power back on to the solenoids, I think it cuts off on addams family if you open the door), then hit the flipper button until it sticks again. Once it sticks, gently push down on it with your hand. If it easily goes back down, then you have an (easy) mechanical reason that it's sticking up.
If you feel resistance, like the game is keeping it pushed up electrically, then you know that you have an electrical problem.
Hopefully it's mechanical; if you lift up the playfield, you'll see a bar to help prop it up with. Turn off the power, and you can see the underside of the flipper assembly. If you use an allen wrench, you can take one of the 'stops' off of the coil; you'll see where the plunger goes through the coil. Take the coil out of it's position, and then look at the coil 'stop' that the plunger hits. If it's all bent up and mushroomed out, that's part of your problem. also look at the end of the plunger for the same thing. You can buy a kit to rebuild the entire flipper assemblys (it will make them much stronger, usually) from
www.PinballLife.com or many other places on the net. If you want to limp by, you can file the mushroomed rim of the plunger and coil stop, then put it all back together. The coil sleeve (plastic, middle of the coil) is probably worn, and should be replaced. I'd get the rebuild kit, but you can clean it and file some things a little bit to make it work o.k. again. One other thing that happens is sometimes the plunger or the coil stop get magnetized, which makes them stick together, leaving the flipper up. A rebuild kit would replace both of them, or quick and dirty you can fix them by beating the hell out of them with a hammer (I'm not kidding, look it up!).
If you have an electrical reason why it's sticking up, it could be that the flipper button contacts on the right side of the cabinet are sticking together, or it could be that a transistor or logic chip is shorted out on the driver board. Since it's only doing it randomly, you've probably just got a mechanical reason, and it's probably just that the flippers are getting worn.