Of course there's all the usual WPC issues, burnt GI connections, reset problems, display issues and so forth.
Specific to ST:TNG, there aren't too many pattern failures. Blown fuses/shorted transistors on the 8-driver board and melting coils to the under playfield diverters and wiring issues in the looms to the cannons are the most common electrical issues. For playfield wear, look around the neutral zone for wear and inspect the clearcoat around the blue inserts in the middle of the playfield for cracking or peeling. The Borg ship dead center in the rear is often melted/distorted from heat off the lamps inside it.
ST:TNG is a pretty heavily loaded machine and one of the most complicated of WPC games. That alone increases the possibility of having a problem. While I've seen and repaired some odd issues with this game in the past, the vast majority of problems I see is what I mentioned above or basic switch/solenoid/lamp type failures that you would see on any pinball machine. Playing the game will pretty quickly give you a good feel for it and any problems it might have.
Cool game, a great addition to any collection!
D