Zombie Cliché Lookout:
In 1990, special effects guru Tom Savini made a surprisingly decent remake of Night of the Living Dead. At one point the now-useful Barbara (in the original she was catatonic for most of the film, and incoherent with fear for the rest) points out that they could easily escape by walking away briskly, seeing as how all the zombies are slow and clumsy. In the end, when the shit was hitting the fan, she made good on her theory by walking away and joining up with some good ol’ boy zombie hunters.
Of course, thinking you’re safe because the zombies are too slow to be a real threat is dangerous in and of itself. In fact, I would argue that this false sense of security is one of the many reasons slow zombies are better than fast zombies.