I bought a STTNG a few weeks ago, heavily routed with a lot of intermittent issues. Mechanically wise, so far I've had:
- check there are only 6 balls in! Mine had 7
- was getting multiple balls launching into the trough and extra balls plunged into play at random points, an LED emitter was out on the trough board (check it using a digi camera, broken they appear dull, should be bright). Also check the resisitors are not broken and the traces are all ok. Empty the 6 balls out, go to you switch matrix and drop a ball in, you should see it pass all 6 optos one by one, then test the VUK into the trough - and check the switch in the shooter lane (mine was bent so not consistently reading right)
- drop target assembly damage. Had to replace frame & eyelet A-14913, and drop target, knockdown arm 01-8647-L. Also adjusted the microswitch so it reads the drop position correctly (check it in switch matrix)
- loose cables on the switch matrix row/column lead to the CPU board. When things got busy multiple rows would activate and the game went crazy. Also pushed in CPU just in case. Not had an issue since touch wood.
- resoldered left VUK opto - check the solder on all of the the optos is not broken, they look ok but if you press the opto you can see it's not fixed
- broken switch on delta ramp - picked up in switch matrix
- new canon actuator which was broken (canon would not turn)
For the trough optos, my next step was to order new ones which are not expensive.
Be sure to read through all the STTNG fix threads on here, I've linked below which I bookmarked. Some really good advice which I never knew was when you go through the switch matrix there is an audible noise telling you when something is not as expected (I never knew this, doh!!). I would advise clearing all the 6 balls out and go through the switches one at a time, if you hear that lower tone beep you need to investigate. Also touch/bang things including the head/cabinet, playfield, toys, etc. and look for flaky switches.
Good luck! Now that my game is running ok (just really dirty) it's a hell of a game
https://pinside.com/pinball/forum/topic/sttng-keeps-giving-2-balls
https://pinside.com/pinball/forum/topic/sttng-top-drop-target-questions
http://www.loriengreen.com/2013/09/pinball-maintenance-star-trek-next-generation/#.V0gKAOS1Z41