Well, first and foremost is she committed a felony by going there. She violated the Logan Act. From Wikipedia:
The Logan Act is a United States federal law that forbids unauthorized citizens from negotiating with foreign governments. It was passed in 1799 and last amended in 1994.[1] Violation of the Logan Act is a felony, punishable under federal law with imprisonment of up to three years.
http://en.wikipedia.org/wiki/Logan_Act
Not to mention that she's not a diplomat...evident by her misquoting of the Israeli Prime Minister.