Check the operation of the related relays, the 5000,etc. Make sure that points are not closing when they aren't supposed to. There is a switch closing somewhere that shouldn't be. I would pull each relay, clean and adjust.

You'd have to find what circuits are sending power to the 1000 point score reel solenoid. Check the following switches to make sure they are adjusted properly and operate correctly:

Score motor switch 1A - switch with red/white wire and red/green wire
Relay switch A - switch with red/green wire and brown/red wire
Thousands unit runout switch - switch with brown/red wire
Relay switch L - switch with red/black wire and brown/red wire
Relay switch M - switch with red/white wire and green/white wire
9th position hundreds unit switch - switch with green/white wire and green/white/red wire
Left target switch - switch with brown/white/red wire and slate/white wire
Right target switch - switch with brown/white/red wire and slate/white wire

One of these switches might be adjusted too closely and a vibration during scoring might make a switch close. Also, check the wire lugs and wires on all the switches to make sure they're not shorting out...