First, whose mistake and who would have been doing the removing?

In my country, our mistake, of course. People were too idealistic during the "Velvet Revolution". We thought that just publicly ending the evil regime is enough, that we can just forgive everyone and have a fresh start. And that the bad guys will be happy for being forgiven (instead of e.g. executed for their crimes) and they will live peacefully.

Yeah... they just waited for a year or two to make sure there is no will to punish them... and then they returned to the power. Since most of the judges or policemen or people in any position of influence except for parliament (because all our attention was focused there) were former communists, it wasn't even difficult. They just had to wait for hedonic adaptation, and blame all the problems on lack of socialism, and then win one election. Then they removed all their opponents from the public media and used the media for propaganda. And used the loyal secret service against political opponents.

I think that in Russia the old Soviet "important people" were effectively removed. The new political elite is not the old political elite.

I don't know about situation in Russia. Just saying that it's not enough to remove the visible people in parliament. It is also important to remove communists from the justice and secret service. Otherwise, you get new faces, connected to the old less visible people.