Stuck On The Bridge
Note to self: when designing a state-of-the-art vessel for missions into the unknown, be careful not to create single-points-of-failures.
On the bridge of TOS, there was only one turbolift ... and apparently, this was the only way out. If a product of 20th century genetic engineering took over the engine room and shut off lift access and life support, you're screwed because manual override rarely works.
After the major refit for the movies, you had at least two lifts. In TNG, there were four. Ship designers got wise to the fact that Starfleet missions might actually involve hostile forces who may try and take over the ship, isolating the command crew in the process.
Otherwise, stuff like this happens:

Hidden escape hatches through the floor might be a good idea.