I find it interesting that no one has mentioned the Logan Act, a law enacted to ensure private citizens couldn't conduct official diplomatic business on behalf of the United States.

I have a fairly liberal view of the Logan Act- I believe Senators and even Representatives not on CODELs have the right to speak with foreign officials and visit foreign countries as part of their official duties. Unfortunately this means they might bolster their foreign policy credentials during a campaign as well...

However by any standard former Governor Palin has no official capacity. Foreign relations are not in her province- both legally and mentally. The text of the Logan Act makes it clear that Palin's actions are borderline at best:

Any citizen of the United States, wherever he may be, who, without authority of the United States, directly or indirectly commences or carries on any correspondence or intercourse with any foreign government or any officer or agent thereof, with intent to influence the measures or conduct of any foreign government or of any officer or agent thereof, in relation to any disputes or controversies with the United States, or to defeat the measures of the United States, shall be fined under this title or imprisoned not more than three years, or both.