Black Holes and Quantum Singularities
Offenders: Lots of shows, but mostly Star Trek: Voyager
Black Holes are interesting phenomena. They are the closest thing we can get to oblivion in the Universe. There are far too many examples of abusing black hole theory to list, but I can address several of the more popular ones.
Black Holes lead to another place in space-time, maybe another Universe
This was a theory for awhile, but it sort of fell apart as people did the math. A Black Hole made of ordinary matter almost certainly leads nowhere but the singularity. See the Black Hole FAQ for details.
You can punch a hole in the event horizon to escape
This was the second or third episode of Star Trek: Voyager where we see the Voyager get trapped inside a “quantum singularity” which has an “event horizon”. Sounds like a Black Hole to me. The writer, one Brannon Braga, decided the event horizon was a force field that could be punched through. Nuh-uh. The event horizon is more of an imaginary line, like the equator. It’s the point where time and space warps so extremely that once you slip past the event horizon, you can’t ever escape.
Actually, you cannot escape from inside an event horizon if you’re restricted to moving slower than the speed of light. If you can move faster than the speed of light (as Voyager is supposed to) then you would have no problems escaping a black hole.
Of course, Janeway gives the order for “Max impulse drive!” in the episode… So they’re not using the space-time warping drive that WOULD allow them to escape.