The case was in the US which is based on secular law. Iran is the one who is imposing their cultural values and understanding of law on the US. Nerve? I agree Iran has a great deal of it. I have listed some of the transgressions you have asked for in my post above. Moreover, the rights that you seem believe Iran has are the very same they do not allow their own people to exercise.
I'm aware that the Trayvon case is based on American, secular law; no need to explain that. I cannot speak for the Iranian government, but their demand for justice for Trayvon is not necessarily "applying" Iranian law to an American case. At least, in their statements I don't see where they cited an Iranian law that would favor Trayvon over Zimmerman. They were simply stating an emotionally charged opinion, probably as a way of attacking the American government, as the American government often attacks the Iranian government. However, saying that Iranians should have freedom of speech or freedom of religion IS applying American law to Iranian life. It's a subtle, but in my opinion important distinction.
In terms of the transgressions you have stated, I have also acknowledged that I do not agree with all of them, or most of them for that matter. One stands out to me; your opinion that their recent elections were not free or fair. Was Rowhani, a moderate who most people felt the Ayatollah would NEVER allow to be elected, was his victory not free and fair? Or if you are referring to the 2008 Green Movement, much of the controversy of that incident was overblown, with foreign media and Iranian citizens alike getting bad information. There was never definite proof that Ahmadinejad rigged the election. In terms of the violence the police committed against the Green Movement, if American rioters were throwing Molotov Cocktails at the White House, I guarantee you our government would react the same way.
You're right though, that Iran commits many acts that one day will hopefully be stopped. However, that is their culture, and it is the culture of many countries in this world. Only they can be the ones to progress and change, and only their own people can be the ones to bring about this change.