I'm impressed, and I'd love to see it in action. But I'm also worried that this is going in the wrong direction. If the law is getting too complex for humans to handle, the solution is not to create supercomputers that help us. The solution should be to simplify the law.
* Jury instruction have been rewritten using the minimum number of terms that jurors won't already know.
* Legal decisions are written to be more readable to contemporary laypeople. (At least they seem that way to me -- it's a little hard to tell given the change in writing styles generally.)
* Uniform legal codes have refactored the law to make it more consistent state-to-state, and to remove complexity when for example two causes of action could be reduced to one.
* Property law (which probably moves more slowly than others) has moved away from centuries-old "magic phrases" that could break inexpertly-written deeds.
But all of this is basically syntax. It makes the system easier to learn, but doesn't reduce the fundamental complexity of the model.
And you can't reduce that complexity much, if you want a system that is "fair" and "just" at scale. "Fair" meaning that it treats like cases alike, and different cases differently. "Just" meaning that it mostly comes to what most people consider the right outcome in individual cases.
The scale here is hundreds of millions of people over hundreds of years, any two (or more) of whom can interact in a way they want the law to settle. Treating all of those cases "fairly" means at least one of: already having a rule that roughly guides the outcome for a given dispute (statutes and regulations), or taking into account the decisions other people came to in similar cases in the past (caselaw). Treating the cases "justly" means those rules and analogies have to be fine-grained -- if one of the parties points out a special circumstance in their case, and most people would feel that it should change the outcome, then it needs to be taken into account for the system to be just.
So law is complex because the potential interactions between hundreds of millions of unique individuals are complex.
You might want to reduce complexity by reducing the reach of the law, but I don't think you can reduce it that far and still have a recognizable society. For example, many libertarians would prefer a system with greatly reduced criminal law and commercial regulation -- but where the government still enforces contract and property law in a way that is predictable and fair. The system for fairly, justly, reliably, predictably enforcing the contracts entered by hundreds of millions of people over hundreds of years is going to be complex -- the same kind of complexity we have now.
Obviously the situation could be better or worse -- the stuff I listed at the top are small examples of how it's gotten better. Making the system (say) half as complex would be great. But it wouldn't fundamentally change the problem space, or make tools like Watson unhelpful for solving it.