Laplace's demon could handle
chaos theory and infinite precision - that is what
perfect knowledge is all about. It is actually
quantum mechanics that throws interesting twists into this. First off, perfect knowledge is possible. Space and time are
quantized - the smallest possible distance being the
Planck Length, and the shortest possible time being
Plank Time. Assuming perfect knowledge, your exact position is known. No infinite stream of decimals to indicate time or place, just use Plank Units.
Indeed, it is a hypothetical construct, just as Maxwell's demon and Schrodinger's Cat. Having a calculator more complex than the universe is not a problem in thought experiments.
Laplace's demon does not make any claims to the existence of God or the number of casual chains necessary for the first cause argument of Aristotle and Saint Thomas Aquinas.
While helping in some ways, quantum mechanics also confuses the issue some. At very small distances and units of time, things become probabilistic rather than deterministic. This makes it difficult to make 100% accurate predictions about the next state of the universe.