Honestly, I probably wouldn't go poking around with a logic probe, unless I had the board out on a bench power supply. A logic probe is only for chip level testing --> 0 to 5v. If you touch anything more than that, like coil voltage, it's going to fry the probe, and possibly damage something on the board. Also, its really easy to short two nearby pins with the probe tip with the slightest shake of the hand. So for me, leaning over a game, stretching to reach something on the game board with the probe, is just too risky.

Proceed with extreme caution.

Do not touch your logic probe to the metal tab of the driver transistors or to a coil with 50 volts on it.
That will surely kill it ( as well as using it in the power supply where you have high voltages for the DMD, not good)

Also, yes be sure not to short adjacent pins when using it. Could cause trouble here and there.

You are pretty much safe using it on TTL ICs on circuit boards.

Cheers and good luck.

Terryb is a pinsider that writes a lot of tech articles. He's got a great tutorial on this subject

http://www.pinballrehab.com/1-articles/solid-state-repair/tutorials/258-using-a-logic-probe

Modern logic probes will handle ttl and cmos, which covers a voltage range of 0-18 volts DC. Keep the probe off high voltage circuits (solenoid/flasher/dmd) and AC circuits.

My logic probe post on pinside covers a couple of pieces of test equipment (minigrabber test clip and DIP clip, which are not covered in the article above) that will make it a lot easier/safer when testing boards while installed in a game.

https://pinside.com/pinball/forum/topic/terrybs-guide-to-logic-probes