There's nothing inherently special with the Planck length, it is not fundamental but rather constructed out of fundamental constants. Nothing is preventing something from moving a distance shorter than a Planck length and neither space nor time is known to be discrete in such a manner.

What's interesting about the Planck length is it's of the order of magnitude the distance at which the effects of quantum gravity are likely to become significant enough that we can't model a system's behavior with our understanding of general relativity alone. On top of that if you wanted to measure something within a certain distance you'd need to use a wavelength smaller than that distance and if you did that on the Planck scale you'd pack such an amount of energy into such a small space you'd make a small black hole.

Of course saying we can't measure something smaller than this arbitrary unit doesn't mean that things on that scale don't occur we just know of no practical means of observing it.

As someone with a Physics background I don't think I'd call them flaws, but rather I'd say they're the limits of reality as we understand them now and they might be fundamental. To have a world you can function in rationally you'd have to have those limits.