Old Testament versus New. "Picking and Choosing"

     So... I know religious arguments are generally viewed as a vain venture in the world of YouTube comments. I usually avoid commenting in general.  But when an argument broke out in the comments of a recent BlimeyCow video regarding how many people find lots of seeming "inconsistencies" in Christian principle.  This was mostly rooted in the age old Old Testament "versus" New Testament discussion.  So I'm leaving my response here to expound on later:

     "I think what frequently gets left out of the conversation is that Old Testament law was not only a religious set of instructions, but also the structure of law for an entire nation.  Ultimately, of course rape, theft, etc was illegal, but when it did occur, it needed to be punished.  Jesus, however, did not come to rule a nation on earth, so no strict legal system was needed.  He left that up to the governments.  He taught, instead, to revere God, and treat others as you would want to be treated."

(YouTube does not allow much room for comments.)

  Questions like "So when someone rapes a woman he only has to pay a fine?", "How is stoning somebody 'loving your neighbor'?", "Christians today wear fabrics with two materials. Wasn't that against the law in the Bible?" are always popping up not only in culture, but within the Church itself.  I can't help but feel like these could be answered much more cleanly and simply than they frequently are, though I could probably have used some streamlining in my own response, too.  It's definitely not too easy.

To be expounded upon.