Incidentally, by default I've already gone beyond all sorts of limits merely be entertaining the idea. As an illustration of the point, the most powerful computers today are often devoted to performing precisely the calculations of Lattice Gauge Theory. The current fastest computers performing about 10,000,000,000,000,000 operations per second still take months to work out what happens in a tiny space of, say, 48 points in each x,y,z direction, taking 32 steps forward in time, where each step is of order 10^-18 seconds and each point is a similar distance apart. To scale this up to the entire Universe implies a computer something like 10^200 times more powerful; to do it in real time probably requires another several orders of magnitude; and since the Universe isn't separated at scales of 10^-18m but closer to 10^-36m again, that ups the required computing rate still further. For any computer we will ever build this is certainly impossible. Obviously then if there is any computer simulation at all it's using no method we can possibly imagine so even entertaining the possibility seriously is breaking current physics in a massive, massive way.
Just about the only thing we have to go on, then, is that the computer is only finitely powerful, and that it stops somewhere. If it doesn't stop, is infinitely powerful and consequently capable of modeling a perfectly continuous Universe with no flaws whatsoever, I don't see how we can test it.