Yes the missing capacitor is absolutely the likely cause of the problem of missed fast hits of the target switch.

These capacitors often fail by going short circuit and cause other problems in the switch matrix. Operators simply cut them out to get the games back up and running but fast hits will sometimes be missed.

Install a 0.047uF 50V capacitor.

The purpose of the capacitor is to extend the amount of time that switches appear as closed between MPU board scans of the switch matrix to avoid very fast switch closure/releases from being missed.
The capacitors are only installed on switches that can activate and release at very high speed such as target switches, pop bumper switches and some rollover switches where the ball can travel very fast over them.

The switch matrix schematic in the manual shows which switches should have capacitors installed.

StarTrek_SwitchMatrix_Capacitors.jpg

Post some pictures of how and where you've soldered the capacitors. Also a picture showing the capacitor value.

I don't see the capacitance value listed on any of the pictured capacitors.
In any case, those are electrolytic capacitors and they don't make them in the low 0.047uf value required in this application. I'm guessing by their physical size you probably have 47uf capacitors or higher which is 1000 times greater than required in this circuit and not suitable.