The author says (and I agree) that the process of judging cannot be easily performed completely by a computer, and goes on arguing for better retrieval systems for legal texts -- so Gödel would probably just shrug.

Actually, I think laws (at least in the Civil Law sense; I'm not too familiar with Case Law) could be adequately represented in some formal logic language if the value judgements are made explicit so that the semantics of the law language specifies the meaning of most operators explicitly but leaves the judging-operator up to human judgment.

Then, laws could be model-checked for loop-holes.