The Problem, A Solution
Ultimately this is why democracy in its current form has failed. We should really be working hard to come up with a new form of democracy, with checks and balances that allow, as a small example, sufficiently large groups of concerned citizens to do something like appoint a special prosecutor to investigate corruption in the government.
Of course, something like that would be easily abusable.
I don't know. I guess the one thing that we could do right now with off the shelf technology would be to assign to each congressperson, supreme court justice, and high executive branch member (president, vp, cabinet secretaries, maybe undersecretaries) a team of people who would do nothing but record on video and audio with multiple redundancy everything those people do, including recording every bit of binary data they generate and getting photocopies of anything they generate in hardcopy. It would become part of truly serving the public, for the years you are in office you give up your right to privacy, much like the way that soldiers give up rights when they sign up for military service.
I think it would be well worth the expense if it would help prevent corruption. If these people want trust they can buy a fucking dog, we need to watch them carefully while they wield the kind of power we've given them.