Some other every-day life scenarios that I think could be plot devices:
- The crew travels back in time to stop a rogue Starfleet officer. They make the mistake of eating at Chipotle while in the 21st century and get food poisoning. The race is then on to stop the rogue Starfleet officer and their own diarrhea before time runs out.
- The crew goes to the annual Running of the Bulls, and the Captain accidentally gets trampled. The CMO must race against the clock to heal his injuries before time runs out. The B-plot here could be that a member of the crew secretly beams a bull aboard, intending to keep it as a pet, but the bull gets loose on board the Discovery, leading to mayhem as the crew tries to contain it before it destroys the ship.
- The First Officer is into doing demolition derbies in his spare time. During one of of those derbies, he takes a hit way too hard, and the car's air bag goes off and bashes his face in. There's a diplomatic summit that he's supposed to go to in two days, and he has to figure out how to present with his jaw wired shut, and his nose in a splint.
- The ship's botanist accidentally mixes poison ivy in with a bouquet of Andorian Blood Flowers presented to the Klingon chancellor. Our heroes must avert war with the Empire after the chancellor uses the bathroom with poison ivy hands, and develops a massive rash.
- The turbolift's certificate of inspection has expired, but the Chief Engineer can't be assed to update it, because all drugs are legal now (see thread about this in this same forum), and he's too busy getting blasted in the Jeffries Tube. The turbolift suffers some kind of catastrophic failure as a result, and crashes through the bottom of the ship. Our heroes must survive in a turbolift car adrift in space until help arrives.