(Sorry for stereotyping but) you're a typical geek. You think that words can have a precise, context-free meaning, and whether something falls within the meaning of a word (or a technical term) can be done in polynomial time.
The real world is much more complicated than that.
Take for example, what is a male and what is female? You'd think it's easy enough to determine that if you have access to the genitals, but there's still difficult corner cases to handle. For legal questions, it can be even more complicated. Questions like "was there a contract?" "is this negligence?" "did the person have the 'intention' to commit the crime?" are simply too 'complicated' to have a deterministic algorithm for all the cases. And before you ask why there are so many lawsuits (I'd imagine many more than the number of people with an indeterminate sex), the fact is that for the vast majority of cases the question is pretty clear cut, and it's really the corner cases that seriously go to court for a dispute on issues of law (as opposed to factual disputes, eg. whether a person did indeed sign a contract, whether the accused did kill the victim, etc.).
Supposedly you can really write out all the anticipated cases in a super horrifically complex program. But then, even if we suppose we can resolve the controversial cases where the facts don't fit our intuition (eg. the many many many situations whether or not you can have an abortion), it defeats the other purpose, that the (general) legal principles should be understandable by a lay person. In fact, lawyers are human beings too (well, not going into the soul question), and if the solution is not understandable by a significant number of lawyers, it's not going to become law. That's where your argument comes in -- but honestly, when you're good at skill X, you'd tend to believe that skill X is all you need to solve the world's problems, until you realize that when you apply skill X outside of its usual domain, it doesn't work in practice. (Just check out the mad scientists cartoons/movies for how things that work in theory could go wrong) The fundamental flaw I see, is that people expect the law to *usually* work according to their *intuition*. Usually court decisions don't tend to go against common sense, and when it does, the legislature will "correct" the decision (at least for common law systems) so that the law is what people expect. The problem is, what people expect can be very self-inconsistent, and what people expect is usually optimized for the normal case, not optimized to reduce the awkward corner cases. If you have no idea what the "self-inconsistencies" of a normal human being is, try understanding a woman. (to please the feminists: or a man who's not a logician -- getting to understand the opposite sex makes you wonder whether everyone's brains are just full of inconsistencies)
And of course you can't just look at the law in its current state and simply declare it void because you have a supposedly better system "intelligently designed" by a genius. I'm not sure about you, but I personally would be very skeptical of any large "rewrite" of a system by a person who doesn't even understand what the system is about.
I do agree there could be a bit more inter-disciplinary research on how CS can assist in making law less complex, but ... from what I know and understand (not to say that it's a lot), I'm skeptical whether there could be any groundbreaking results.
I'd say, getting legislation to use a proper version control system, and if a git-blame could show all the people who voted for/against a particular law, it would already be a great win. :)