What causes a weak flipper on a 1980's pinball machine?

a flipper usually has two windings. One winding is higher voltage then the other so it results in making the flipper paddle hit very hard. Then the second winding takes over and a lower voltage is used so the flipper coil doesn't get damaged by someone holding in the flipper button. There is a switch near the coil that is called the end of stroke switch which turns on the lower voltage. So a couple of things can cause a weak flipper.
1. the end of stroke switch is dirty and not making contact causing the flipper to operate on only the lower voltage
2 a broken wire on either the coil or end of stroke switch
3. the high voltage winding on the coil is damaged.

It varies slightly from machine to machine, but the flippers are basically driven by Soleniods (magnetic coils and a plunger.) the coils often have a Diode pack across them to allow faster release. The diode pack could short out reducing the amount of current available to the solenoid which slows it down. You can test the voltage across the two pins on the flipper solenoid.

You might even just need to clean the plunger and the contacts to the wires may have built up oxidation.

Try swaping the solenoids between the two flippers and see if the problem moves with the solenoid. If so replace the diode pack and/or solenoid.

The most likely cause is a bad coil. It could also be a voltage problem to that coil. Other things to check are the bushings the flipper goes through on the playfield. Clean and lubricate.

The solenoid plunger (the thing that operates the flipper) may be rusted or dirty. Rusted ones should be cleaned with steel woll, a dirty one should be cleaned with rubbing alcohol. DONT oil or grease the shaft it will most likely gum up the mechanism and/or attract dirt-and could possibly short circuit the coil as well-unless lubrication is specifically recommended in the game manual. The sleeve may need to be cleaned or replaced as well, so if the problem remains, you'll have to take the flipper mechanism apart (one at a time so if you really screw it up you can look at the other one) and remove the sleeve. You don't neccesarily have to remove every single piece-you may be able to just unscrew the plunger from the rest of the mechanism-then unscrew the solenoid itself. DON'T force anything. Don't worry, you should be able to put the solenoid back in straight via the screw holes-if they're worn too big to hold it in place, that may be the cause of the weak flipper. Unfortunately, nothing much can be done about that. Anyhow, remove the sleeve and plunger and then stick something through the sleeve. If it comes out dirty clean the sleeve, if it looks very very rough on the inside or is cracked or otherwise damaged, they are likely dirt cheap to replace so if in doubt, swap it out.

I don't know if the plungers themselves retain a magnetic field so I wouldn't recommend putting them near anything that would be affected by magnets-memory cards, CDs and tapes or anything with a COLOR screen (black and white screens, such as calculators, watches, etc won't be affected)

Overuse.