How can we improve the judicial system that monitors our politicians deals (spotting for fraud, corruption) when it is not in the interest of anybody involved?

Historically, Guillotines

In a nutshell: https://terikanefield.com/criminallawfaqs/

I would advise reading that page in order, and in full. It lays a lot of foundation as it goes. There is indeed a call-to-action at the end.

Our system resembles an obstacle course. One consequence of the hard work of people like Thurgood Marshall is taking power away from law enforcement and subjecting law enforcement (including prosecutors) to stringent rules. Federal Criminal Procedure is a full-semester law school course. It is mindbogglingly complex, but keep this in mind: The complexity is to create fairness.

Dear people who want the process to move more quickly: Be careful what you wish for. Giving more power to law enforcement (and prosecutors are part of law enforcement) might bring about the short-term results you want, but is not a good idea in the long run.

People talk a lot about single payer healthcare, but some legal scholars propose a single payer judicial system. I.e. private lawyers are banned, and everyone must use publicly funded lawyers.

This would make prosecution accessible to the masses, and successfully defending not related to how much money you have.

By making sure a lot of people have a small stake in it, and making sure that everyone involved is afraid to be fired if things are not properly handled.

The judicial system in my country, Portugal, is a moderate example of success (when it comes to not being too partisan, effectiveness and speed is not good, mostly due to legislative and governing incompetence, and incompetence from public prosecutors), but the basic way it works afaik is that the superior council of magistrates, which is tasked with supervising judges has a 40% stake internally elected (by other judges), a 40% stake by parliament and a 20% stake by the President.

Because the government is parliament bound and is NOT the President, then the executive power is separate from the president.

Finally, here the president has a more “cerimonial role” with his real power being fundamentally to be a last resort when all turns to chaos. So far it has worked well-ish

the judicial system

Which one, Andorra, Belarus, Cuba, Danmark... where are you?

https://anarchistfaq.org

Don't give up. It might sound like a cliché: This not something that is won overnight.

It's either that or revolution...

Everything starts with you engaging in local politics.

You get the politicians your deserve.

If you don't engage in the local part of the political party that is closest to your views, then someone else will. That "someone else" might not have the same good intentions like you do.

The politicians elected in the lower parts of the political pyramid are the ones that will eventually rise to the next level.

So the corrupt ones in the top could have had a much harder journey if people stop focusing on the top and change focus to their own surroundings.