Tighten the screws on the counters, after that adjust the contacts so that there is a slightly "wiping" motion at closing and opening.
One of the three contacts is not adjusted right, they have the current to step back, but the index contact is not closed or making bad contact.
Index and current are the two top contacts, closed at position 1 to 9 and open on 0.

Hi Walt, wizardblom +
to support wizardblom I visited: http://www.planetarypinball.com/mm5/merchant.mvc?Screen=BOOK , Bally 1976 Parts Catalog and in that Catalog: http://www.planetarypinball.com/reference/partsmanuals/BLY_Parts_1976/index.html#/114/ (on the bottom to the left there is a "magnifying glass" You may want to use) - I made 3 snapshots - put together and made a JPG - above the 3 Switches to check: I made an rectangular green mark.
TWO Switches OPEN in Zero-Position, ONE Switch "is ONLY-CLOSED in Position-9". Look at a "good Score-Drum (player-2,3,4)" - LOOK for broken-off wire. Greetings Rolf

aBally-Score-Drum (resized).jpg

Hi Walt
Your observation (post-1) is valuable - "problem does NOT show up on first-player-Score-Drum-10-90". Look at the first JPG (made from ipdb-schematics): The 10-90 is resetted (stepped forward) by a "Switch on Number-TWO-Reset-Relay" - the OTHER Score-Drums of player-1 are resetted by "Switches on Number-ONE-Reset-Relay". (Because of "logic in the pins") I do not believe that the problem is in the "Switches on Number-ONE-Reset-Relay" - well, I would have to make a very wild hypotheses.

Look at the second JPG (((I colored plenty of stuff because I would like (later) to do some "theory - reading schematics" - I guess that You are in the mood for troubleshooting, so))) look only at the lower-right corner. The "drawn abstract" schematics shows (bottom-middle) "16 Drum Unit Zero Position switches" - but drawn is only "one such switch" - as the 16 Switches are mounted PARALLEL***. Look at the lower-right corner - maybe in reality in the pin the wiring is "MY drawing" - IF (if) at "my violet X" a wire has broken-off from a solder-lug: YOUR PROBLEM.

Watch out for wire-30-yellow and for wire-48-8-green-black as they come to the "Zero-Position-Switch(es) on the Score-Drums of player-1 --- gently grab the wires and pull a bit - soldered-on or broken-off ? Check ALL FOUR Score-Drums of player-1, greetings Rolf
P.S.: See "mounted in series" and "mounted parallel***" in the second JPG.

zOld-Chicago-Work-6 (resized).jpg

zOld-Chicago-Work-7 (resized).jpg

Hi Walt
great - problem solved. So we can (at leisure, relaxed) do some "reading schematics". You had the somewhat strange phenomena "when starting a new game: Some Score-Drums do sometimes NOT reset (but sometimes they do) --- toggling off the pin - toggling-on, starting a game: NOW these Score-Drums DO reset" --- strange ? No - we can see it in the schematics

"Short" explanation - The maximum of "steps to do" when "resetting a Score-Drum" is NINE steps (accidentally the Score-Drum shows "1" or "10" "100" or "1000" - must be stepped forward NINE steps to reach "Zero-Position"). Lets have a pin in state "Game-Over" - we press the Replay-Button - some stuff happens - then the Score-Motor starts turning, the Reset-Relay pulls in, the "Number-1 / Number-2 Reset-Relays" are pulsed by the turning Score-Motor - the Score-Motor has its own switch to guarantee "a turn will be completed" - another switch on the Score-Motor KEEPS the Reset-Relay pulling until the turn is completed.
When the Score-Motor makes a turn: FIVE pulses of electricity are fired - EVERY Score-Drum makes up to five steps (maybe less as a Drum reaches early its "Zero-Position").
The "faulty" Score-Drum does NOT signalize: "NEED another turn of the Score-Motor to completely step to Zero-Position" - the Reset-Relay drops out and the Score-Motor stops.

You toggle-off and You toggle-on --- THIS MAKES THE GAME-OVER-RELAY TO MOVE INTO "beeing in state Game-Over, means the relay TRIPS (done when You toggle-on)" --- You start again - the faulty Score-Drum NOW has a maximum of FOUR steps to reach Zero-Position - FOUR is less than FIVE - when starting another new game: The turn of the Score-Motor gives us (as always) FIVE shots of electricity - the "faulty" Score-Drum completes the "stepping forward to Position-Zero / resetting".

Look at the second JPG in post-4 - the succession / sequence in time is: "light-green" - "dark-green" - "light blue" - "medium-blue" - "dark-blue".
Please read here: https://pinside.com/pinball/forum/topic/bally-night-rider-em-problems-em-rookie#post-3393986 - read on the bottom: "The schematics shows ..."
We look HERE at the JPG in post-4 - "encircled light-green Switch on Game-Over-Relay" - the Switch is drawn "open" - but as the pin is in "state Game-Over": SWITCH is closed.
You press the Replay-Button ... Coin-Relay pulls-in and closes its "encircled light-green Switch", "encircled light-green Switch on Game-Over-Relay" is closed (as in reality the GO-Relay has tripped) --- the (encircled light-green) "Coil on Reset-Relay" pulls-in - closes its (encircled dark-green) Self-Hold-Switch.

Not in the JPG: The Score-Motor is started - by turning the "encircled dark-green" Switch SCM-1C closes for (((almost))) to the end of the turn --- THIS SWITCH makes the Reset-Relay STAY PULLING for the rest of the motor-turn - happily (encircled light-blue) the Number-1- / Number-2-Reset-Relays accept through SCM-2A and SCM-11B the five pulses - they fire and make the Score-Drums step.

At some time the Game-Over-Relay is latched - and the Coin-Relay quits pulling. At the end of the Score-Motor-Turn the "(16) Drum Unit Zero Position Sws" should make the Reset-Relay stay pulling - so the Score-Motor does make another turn - so again five shots of electricity to step the Score-Drums - but faulty no signal "make another turn": The end.

You toggle-off the pin - toggle-on the pin - this makes the Game-Over-Relay TRIP - moving into "state Game-Over" - You press the Replay-Button - the "written above" takes place again - the "faulty" Score-Drum only has up to FOUR steps to do - so by now (FIVE shots are delivered): The Reset will be completed.

"medium-blue" stuff - After pressing the Replay-Button - at the time the "green stuff takes place": ALSO the "medium-blue" stuff takes place: The Replay-Counter-Wheel is stepped down one step, and because the Reset-Relay is pulling: The Coin-Unit-Reset-Solenoid fires and brings the Coin-Unit into position "ONE Player wants to play" (((in the ipdb-schematics: To the right of "Coin-Unit-Reset-Solenoid" is drawn more stuff: "Ball-Count-Unit / Player-Unit / Game-Over-Relay to be put in proper position".

"dark-blue Coin-Unit-Step-up-Soleniod" - hmm, I may have distracted / confused You - so well, here : Some more theory. IF (if) a game has been started - everything is resetted and the ball is in the Shooter-Alley ready for a ONE-Player-Game --- You then press the Replay-Button - the pin just steps the Coin-Unit up to "TWO players want to participate in the following game".
The Game-Over-Relay is latched (pin has resetted, ready for a 1-player-game) - the Reset-Relay therefore does (another pressing of Replay-Button) not pull-in - therefore no resettting of Score-Drums - through the pulling Coin-Relay and the non-pulling Reset-Relay the "encircled dark-blue" coil fires and TWO players can participate.

Please ask when You want more information - and we look at an specific step in this complicated "starting and resetting for a 1-player-game", greetings Rolf

I'm having this same problem with my Old Chicago, thank you Rolf - I know where to start looking!