I'm not sure if GP's suggestion is actually viable (the whole "who watches the watchers" problem, and there is no way funding to the new department could match the existing departments - ie at best, it will not be that effective).

However, I've always thought that judicial system is a mean to check the legislative branch (rather than executive). The reasons being that judicial system has no mean to enforce/ prevent wrong doing (legislative can cut funding), and they also have no way to proactive prevent any wrong doings from happening (you can't do investigation, and anything that reaches the court necessitates a lawsuit).

The Judicial checks the Executive in that the Executive is tasked with brining people before the Courts. The Courts decide if that person should be punished in accordance with the laws, but they can also rule on the behaviour of law enforcement in accordance with the laws too.

I've wondered about that angle too. Maybe the Judicial branch should have its own enforcement arm. SCOTUS does have its own police force.

Sure, provided that you are independently rich.