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Well I guess the two most important objections to this brand of determinism are scientific ones.
1. Chaos Theory
2. Quantum Mechanics
Chaos theory shows how exceedingly difficult it is to make predictions for non-linear systems. You might intuitivly belive that if we have a model of a system, with inititial values 99.9% accurate, you would expect to get precistions as accurate or say reasonably accurate say 90% accurate. Chaos theory shows that this is not the case. In order to get accurate results, you would in fact need to have incredibly accurate initial measurements...and even then your predictions will only be valid for a short time into the future. If you want to make predictions for an arbitrary length of time, you will need initial measurements 100% accurate! (Bear in mind that a number to signify the position of a single particle would have to be infinitely long!).
Quantum Mechanics shows that nature appears to be random at heart...not nicely deterministic like Newtonian mechanics. Some people attribute this randomness to our lack of information about what is "going on down there", others believe that unpredictability is an objective property of nature. The jury is still out on this one, although the current scientific thinking tends towards randomness as something real.
Both of these things paint a pretty grim picture of our ability to predict relatively small things, let alone an entire universe.
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