Don't forget that thing about "Let he who is without sin cast the first stone".
Adultery was still a capital crime when Jesus addressed the woman caught in adultery. It would have been a misapplication of justice for him to have her stoned because the man was not also presented to him. The law, which was still in effect for such crimes (just as it was for murder and sexual deviancy), has stringent and exact requirements which requires BOTH of them to be brought forward.
I don't know how people can think that the law is somehow magically done away with. The law was never intended to save us, but to teach us about sin and make sin "exceedingly sinful" according to Paul. Paul frequently talks about sins "unto death." Adultery is one of them. Murder doesn't get a pass either, nor does sexual sin. The only parts of the law not in effect are those that deal with sacrifice and carnal ordinances which were fulfilled by Jesus. See Hebrews 9:8-10:
8 The Holy Ghost this signifying, that the way into the holiest of all was not yet made manifest, while as the first tabernacle was yet standing: 9 Which was a figure for the time then present, in which were offered both gifts and sacrifices, that could not make him that did the service perfect, as pertaining to the conscience; 10 Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation.
"...until the time of the reformation", that is, until Christ has come.
Finally, constructions with "Let" require the subject in the objective case:
Let HIM, who is without sin among you, cast the first stone.