+5
I keep thinking of more.
Cars working after the apocalypse.
Batteries go dead after a couple of weeks, but even if you somehow charge them, gasoline only lasts a year before going bad. Surprisingly, the Mad Max series is the most accurate. You'd need sources of oil in order to keep gasoline in your vehicles.
While on the subject of apocalypse shows/movies, who the hell is mowing the grass everywhere? I haven't seen a single overgrown lawn.
Dynamite being completely inert until the fuse is lit. Dynamite is filled with nitroglycerin. It's extremely dangerous to work with, often exploding for no apparent reason. I can only remember two movies where this happens: Saving Private Ryan, and Journey of Natty Gann.
Adam and Eve scenarios (more common in older Sci-fi and fantasy), where a small group of people repopulate a planet. You need hundreds, if not thousands of humans to have enough genetic diversity to survive.