From a comment earlier but worth discussion: “Seems our whole system of “checks and balances” has a weak spot - the judiciary is not accountable to anyone but themselves, unlike the other branches. Once they’re entrenched it’s hard to remove them, and there’s no periodic review of their rulings and what type of cases they choose. It’s a place where corrupt or subversive elements could get into and hide out.”
Other than initial appointments, what checks and balances are there on the judicial branch? How could the system be improved moving forward?
That's not true at all. In the case of federal judges including the supreme court, first they need approval from congress before serving, and anytime afterwards Congress has the ability to impeach them.
The checks are real, they're just not used often. And having a corrupted Congress doesn't help, and means the controls will never be used to help the people.
For states, you should check the state constitution. California impeached their supreme court chief justice many years ago, with a ballot resolution after the state legislature never followed up. (Rose Bird, a real crazy commie.)