I never found the Enterprise falling apart very funny either. The level of malfuction was almost as bad the Iconian computer virus that destroyed the Yamato.
Well, not actually. The only actual mission-critical thing that wasn't working was the transporter, and very clearly that was a touch-and-go case which might be reasonably expected to be working by the time they reached Nimbus III. In any case they had an acceptable alternate way to rescue the party through the shuttlecraft.
It's awkward when the turbolift doors don't open smoothly and the ship's log recorder is all twitchy, but you don't need them for that sort of rescue mission. You need warp drive, sensors, shields, photon torpedoes, and these were all just fine. Phasers would probably come in handy too, but I don't think we get any word about ship's phasers.