in the wikipedia article on "The Problem of Hell" it talks about the unfairness of an infinite consequence of finite sin. Regardless of how bad one was on earth, nevertheless an infinite punishment for sins committed during a finite period seems an overkill.
On the other hand, is it fair that an entire lifetime is altered just by a 1 hour exam? Or that one mistake could land you the death penalty in the wrong country?
What are your opinions on this, as I am quite troubled by it.
The first thing I would ask is: In exactly what sense is a sin finite? The sense in which Hell is infinite is duration, and since there is no going back in time and changing the past, as far as I know, it would seem that sins are infinite in duration also since they cannot be undone. Both are therefore infinite and the argument is invalid.
Secondly, people are not sent to Hell on the basis of their individual actions anyway, but rather the motivation behind them, so the argument is again invalid. Regardless of how "bad" of a person you are, you can still go to Heaven if you repent and trust in God. Even the so-called "worst" people to have ever lived, such as Hitler and Stalin, could be saved if they would have repented. It doesn't matter what you've done in the past, if you repent and trust you will be saved.
The reason people are sent to Hell is because they are intent on following their own rules, rather than God's rules. Atheists, for example, have their own morality that they adhere to. They may agree with God on some things, like murder, but on other things they disagree, and whenever they disagree they simply ignore what God has to say. Obedience only when you feel like it is not obedience at all.
If unbelievers are simply going to ignore God and follow their own morality here on Earth, what reason is there to think they would do any differently in Heaven? If such people were in Heaven, Heaven would be no different than Earth. It would be full of people refusing to obey God and instead following their own desires. That would defeat the purpose of Heaven entirely.
The ONLY way to get in to Heaven is to submit to God and follow his rules. This is why unbelievers can never please God. Even when unbelievers do good things, they're only doing so to please themselves, which is not pleasing God. This is also the reason why Heaven will be perfect, because God's rules are perfect and everyone in Heaven will be following God's rules.