The concepts of causality, free will, and morality will be unaffected for the most part. Most of the discussion on those topics assume that there is something more than the continuous physical world, so a shift to a discretized physical world would not cause much of a shift in discussion. Obviously the discussion which does focus on the continuous physical world would shift... in particular the discussion of free will if one assumes there is no metaphysics will get interesting, but it's interesting already!
One thing that would change is any discussion of chaotic systems. Right now, it is believed by the majority that we exist in a 3-dimensional Euclidean space, with one dimension of time. In this continuous environment, chaotic systems can form from a finite number of linear components. If it were discretized, one is obliged to either have nonlinear components, an infinite number of components, or chaotic systems cannot form. Given that most of the rules of physics we are familiar with are defined in linear systems, this would be a big deal.
How much would this affect the greater discussion on those topics? Probably not all that much. It is a hot point for me because I have seen reasons to argue that one of the challenges of identifying a metaphysical "consciousness" is that we cannot define it in a way which excludes all purely-physical chaotic systems. Phrased another way, it appears possible to construct a P-zombie using chaotic systems. If it was possible that the rules of the universe prohibit true chaotic behavior, it would be possible to define a test to separate the purely physical from any metaphysical consciousness, answering once and for all whether we, ourselves, are concious. However, that is not a widely held opinion, so it should not be thought of as a statement about the wider discussions on freewill.