What is the verdict on an unjust judge?

The trivial answer is the correct one according to the Christian view. Under the correct circumstances, the price has been paid.

I think the premise of your question is a bit off though. When someone or something has to judge something, they also have to judge it for a particular purpose. When a criminal court judge decides whether someone committed murder, it is for a particular purpose and to a particular standard adapted to that purpose. If you had to judge whether a person committed murder for some reason (maybe to decide whether or not to trust them with your life), you are judging for a different purpose and there is no reason you need to use the same standard. You don't have to swear in witnesses, follow written rules of evidence, and so on.

So I don't think it's sensible to just compare the kind of judging that goes on in a court with the kind of judging Christians hold that God does without taking into account the vastly different natures of the judges and purposes of the judgment.

First off, we must remember that we and any other human judge can only observe a person's deeds, and we can end up not seeing some of those, either because we didn't notice or weren't around, or because someone actively worked to hide them from us. But God sees everything that people do, and he can know the thoughts of their heart, which gives him a much better perspective and makes him the only one qualified to render a truly objective judgment. What does not appear fair to us from our limited perspective may indeed be something we would agree was fair if we truly had all the information.

Second, God's forgiveness isn't some instant and painless thing. It requires repentance. There are two different terms in the Bible translated as "repent," which is kind of unfortunate because they're very different words. In the Old Testament, the original word refers to sorrow, and is often applied to God himself, who of course has no sins to repent of. But the New Testament word, used in the context of the Gospel, refers to change: A change of heart, a change of one's ways, and when possible finding some way to make up for the damage that was done.

This is why murder, harm to innocent children and certain sexual sins are considered particularly grievous: once done, they cannot be undone! If I steal from my neighbor, I can give back what I stole, but if I kill him, that's final, and so very difficult to repent of and find forgiveness for.

Once a person has sincerely repented of their sins, then it is possible for them to be forgiven, through faith in Jesus Christ and the power of his Atonement. Jesus took our sins upon himself and suffered the just punishment of the laws of God, so that those who would believe in him and repent could find forgiveness and reconciliation with God, as explained in Romans chapter 3. So the basic answer to the question, "how can God forgive a sinner without being unjust" is that the sin has already been paid for and the law of justice satisfied, thus making it possible for Christ to show mercy on those who have faith in him and repent of their sins.

If an earthly judge --charged by the state to uphold the laws of the state in a fair manner and himself known to be a good and upright judge-- were to knowingly acquit a guilty party we would rage against him.

The key here is that God is not only the judicial branch, but also the executive and legislative. When a judge presides over a criminal trial, he is hearing evidence of crimes not against individuals, but the state. Murder is horrible to the individual and family of the victim, but the perpetrator goes before a judge because the state also outlawed it and decided to take it personally.

The state, in the person of the executive, has a similar power of pardon that is sometimes used. Now, if God were to go pardoning everyone willy nilly that would be one thing, but thankfully it does not happen this way. We have an intercessor in the person of Jesus Christ. He gives evidence on our behalf, that we have repented and that price for our sins have been paid.

The key consideration is the definition of justice. Does justice necessitate punishment or restoration? If I steal $100 from someone, I don't need to be physically beaten. If I repay the amount--or even 7 times the amount--the offended party is restored. If another person pays that amount on my behalf, the offended party is still restored and would have no right to demand further punishment of the one who stole.

As we stand before God, it is God who is the offended party. God's holiness is restored through the infinite, matchless, all-encompassing payment of Jesus on the Cross. The death of Jesus was more than 7 times the payment in retribution to the offended party. Though this payment is made on our behalf, the offended party is restored, and God lays no further claim on our sin.

So, God is, indeed, just in His requirement of a payment. The debt is fully paid and then some. He would be unjust if He still laid any claim of sin on those for whom the payment has been made and received.

The holiness and justice of God is so infinite that the smallest infraction demands restitution. However, the death of Christ on the Cross is such an infinite payment that it can completely cover all the offenses of the worst sinner.

Alright, here's the non-trivial answer.

The idea is that we are all guilty. It's pretty hard to deny this one:

Romans 3:23 (NIV)

for all have sinned and fall short of the glory of God

Furthermore, while we are all guilty of sin, the punishment for this sin is death:

Romans 6:23a (NIV)

For the wages of sin is death

If we go on in Romans 3, we see that the Jesus was the atonement for our sin.

Romans 3:25 (NIV)

God presented Christ as a sacrifice of atonement, through the shedding of his blood—to be received by faith. He did this to demonstrate his righteousness, because in his forbearance he had left the sins committed beforehand unpunished

Definition of atonement

satisfaction or reparation for a wrong or injury; amends.

So, we can see from Romans 3:25 above that Christ was the sacrifice of atonement for our sins.

In essence, we are guilty of the sins that we commit (Romans 3:23 at top). Because of those sins, a price has to be paid (Romans 6:23a). Since the price had to be paid, Jesus was presented as the atonement sacrifice. (Romans 3:25). We can receive this atonement by faith (Romans 3:25 again).

Furthermore, this debt had to be paid to show that he is just. God is both just and righteous--being the one who deals the justice as well as the one who justifies (through the atonement for the sin).

Romans 3:26 (NIV)

he did it to demonstrate his righteousness at the present time, so as to be just and the one who justifies those who have faith in Jesus.

Summary

God is a just God; He requires a penalty be paid for the sins we commit; and Jesus is that atonement for those sins.

Tying this in to my trivial answer, our sins create a debt that must be paid (just as our breaking the law creates a debt to society). However, this debt has been paid already if we have faith to accept the grace given to us.