Doesn't seem like anyone even asked what type of punishment system the Edo had, in the event one of the crew inadvertently broke a law. They were too excited to get down to the horny planet.
Or maybe they did ask, and the Edo didn't answer.
Yeah, and naturally, this very important duty would just be dropped at this point...
Yar: Yeah, listen we've been reviewing your laws and we can't find anything about actual punishment for crimes. Could you fill us in?
Edo Representative: No.
Riker: Sounds safe to me, Lieutenant. Let's go, I have a date with that one blonde tonight.
The Edo may have been dicks about this, but the senior staff of the Enterprise shouldn't get a free pass for being stupid.