The 10 ohm resistor is there to drop the voltage to the Q relay after the Target relay that fired it in the first place drops out. In other words, the Target relay is only active as long as the ball is closing the the target switch. The Q relay fires at the same time since it's in series, but needs to stay active through the end of the Score Motor cycle so the 500 points can be added. The resistor and the lock in switch on the Q relay are what keep the Q relay active until the Score Motor 2B switch opens.

All of the relay coils in this part of the circuit are designed to operate at less than the full 25 volts since they're wired in series. Without the resistor in place the Q relay would see less than 25 volts when it fires in series with one of the Target relays, but would see the full 25 volts as soon as lock in switch closed. The resistor drops the lock in voltage down to an appropriate level.

The 500/5000 point scoring dilemma looks like a race condition. If things happened instantly you could imagine an order of events where the wrong score would be added. Your theory that the targets are wired so that one switch closes before another is interesting. You could test that theory by shorting one switch or the other behind a target to see if you could get the wrong score. I bet you can.

What might make this reliable is the fact that things don't happen instantly but take a certain amount of time. So for example if the E relay can fire in less time than it takes the Q relay to fire and to open its closed switches that would be enough to make it reliable. Putting the E relay switch on the targets in front of the Q relay switches would certainly help bias things in that way.

/Mark

Race condition is an engineering term used to describe things that don't predictably complete the same way every time.

As a wild assumption pick a ball speed of 10' per second (about 3 playfields per second?) and a target switch gap of 1/32". In that case it would take the ball about 1/3 of a millisecond to travel far enough to close each switch. So one should close about 1/3 of a millisecond before the other. That can be a lot of time in electrical terms.

Experimenting with closing the switches out of order might prove your theory.

Be wary of Make/Make switches behind targets. I've encountered a couple (one here on Pinside I think) where the two outside leaves were incorrectly wired onto the first two leaves of the switch and the middle leaf was wired to the back. What happens on a light hit on the target is that only the first two leaves touch making a connection between two parts of the circuit that should never be connected together without the third leaf also being connected. Most of the time the target is hit hard enough to close all three leaves together so it makes no difference if they are wired out of order.