Mitt Romney, whether he knows it or not, now has stature, and to some extent speaks for the United States. His prestige is approximately that of the Vice-President, Secretary of State or First Lady. The role he plays overseas is very different from the one he plays in the US. Here he's allowed to be scrappy and highly critical of the President. That's our system working, as long as he's being truthful, and of course that's been a problem.
Overseas, we're all on the same team. It's about keeping the country strong, and that's something Romney believes in, if you take him at his word. If a foreign leader were to get the idea that he or she could choose who they negotiate with, then the US is only one half as strong as it would be if there were only one go-to guy. If 25 people have equal power, then each represents a country with the sway of a third-tier power. Gone is the power and prestige of the United States.
The only way it works in favor of the United States is if we are united. Work out our differences here, and all our power will be represented overseas. But we only have one President at a time. And if you're playing on our team, you have to respect the wisdom of that rule.
Romney, overseas, should do what he does so well -- smile -- and say nothing. Wave, shake hands, privately make $10K bets on trivial stuff, slap people on the back, and promise to pass the message to the President when he gets home.
PS: With future candidate trips it might pay to send the sitting Secretary of State along with them, in case any of the world leaders want to talk business.