Can a Jew forgive a Nazi? Take for example Simon Weisenthal, who was asked mechila by a dying SS guard, as the representative of all Jews.
A Jew can forgive a Nazi, but he cannot do so on behalf of others, and only on behalf of himself. If the Nazi wronged the particular Jew in question, the Jew would be able to forgive him; if he wronged others, only those others can forgive.
The question of whether he should forgive a Nazi depends very much on the circumstances, and of course it would only arise if he is convinced that the Nazi has truly repented, sincerely regrets his past ways, and is ready to somehow make amends.
Even when a person truly asks for forgiveness, and regrets his ways, forgiveness is only true if it is sincere. There are some crimes, some offences, that are too heinous for a person to be able to forgive, even if he really wants to. If this is the case, then saying “I forgive you” does not have much significance. It depends more on what is in the heart that what is said by mouth. Rather than a technical matter, forgiveness is a matter of healing a torn relationship; sometimes, the tear cannot be mended.
For instance, a wife will find it hard to forgive a cheating husband the day she finds out about his infidelity. However, after some time, she might be able to truly forgive. Thus, if a person cannot forgive at a certain stage of his life, then he cannot–but he can give the other hope that perhaps sometime in the future, he will be able to forgive.