> Judges interpret the law.

That is possible only if you actually know the law. If you do not know it, you cant interpret it.

So yes, people are needed to interpret the law, but not really anyone. Kinda like we need programmers, but not really anyone.

It is possible for competent programmers to interpret a vaguely written specification in mutually incompatible ways.

Yes, although the judges in the OP do not sound analogous to competent programmers in this example. One would expect someone trained in software to interpret software, in the same way one would expect someone trained in law to interpret law.

I find it hard to believe that programmers could disagree with eachother.

>If judges in a jurisdiction are elected, it is the responsibility of the electorate to make sure the judges they select are the most qualified (perhaps by studying previous decisions, academic publications, etc). Analogously, if judges are appointed by other elected officials, it is the responsibility of the electorate to select public servants who are good at appointing competent judges.

Responsibility is not a zero sum game. Voters and officials who elect and appoint judges are responsible for their actions just as much as judges are responsible for upholding and following the law. While many areas of the law are ambiguous and up to the discretion of the judge to decide, many other areas are well-established and clear cut (such as the illegality of jailing defendants who have not had access to a lawyer). The fact remains that we cannot exist as a society that depends on the rule of law to function if we have judges and other officers of the court who are unwilling or incapable of upholding the law as it exists.

While your statement is technically correct, it does not address the issue.