Every once in a while an epiphany hits you that's been staring in your face for thirty years.
In John 8, Jesus did not forgive the woman who was caught in adultery. Rather, he maneuvered her accusers into dropping their charges against her. Different thing entirely.
With no eyewitnesses to testify against her, there was no case, and she was acquitted (or rather, pardoned - she was guilty, after all).
Yet Jesus perceived that she really was guilty, so he did the only thing left for him to do: he told her to "Go, and sin no more."
The story wasn't about her being forgiven by God; it was about saving her life in the culture's legal environment. Jesus wasn't asking the accusers to forgive her; he was asking them to cool off enough from the mob mentality to make sure they really wanted to testify in a case that would lead to the death of a fellow human being who in retrospect wasn't any more sinful than they themselves were.