It is well known how to represent arbitrary-precision decimal numbers in a computer, so I don't get your point about precision of counting. Furthermore, the fac

It is well known how to represent arbitrary-precision decimal numbers in a computer, so I don't get your point about precision of counting. Furthermore, the fact that the simulating computer stores the state of our atoms in some kind of floating point doesn't mean that when we think about the concept of numbers, we are limited to floating point. The abstraction capability of the human mind means that we can think about numbers that are larger, or more precise, than any physical magnitude in the universe. It is easy to write a number way larger than the number of elementary particles in the universe, and we don't make the universe overflow when we do that. In fact, we know that there are limits in our world to how small a physical magnitude can be - Planck's time, Planck's length, etc. This seems quite coherent with a computer with finite memory simulating our world. If the guys creating the simulation have enough resources and skill (superhuman beings from an external universe wouldn't necessarily make bugs when coding) I don't see why we would notice any glitch. Even more so when the part of the universe that we perceive is relatively tiny, and anyway the set of things that we can and cannot notice may be determined by the program itself.