For many of his opponents, Mitt Romney has been a lot of fun. The Republican presidential candidate has supplied dozens of lame and comically awkward moments – from tying the family dog to the top of his car to boasting of knowing Nascar racing team owners to putting a car elevator in one of his homes. These episodes and many more have sparked much mockery of the multimillionaire for being pathetically out of touch with how real people live.

But after what pundits rate as a win in the first presidential debate, and the ensuing ratings bump in a major poll, it's time to consider a fact: Mitt Romney stands a chance of moving into the Oval Office next January.

That doesn't just matter to Americans. With the US still the largest economy and military power on Earth, what happens in Washington does not stay in Washington. And now that Romney has given what his campaign described as "a major foreign policy speech", laying out why he thinks "the 21st century can and must be an American century," it's time for the rest of the world to consider what President Romney would mean for them, too.

Many analysts say the speech was long on tough rhetoric and short on specific policies. But here's a snapshot of what Romney said he'd do in these key areas:

1) Syria: he'd arm the rebels

Romney criticised President Barack Obama for not supporting the Syrian rebels forcefully enough and pledged to "work with our partners to identify and organise those members of the opposition who share our values and ensure they obtain the arms they need to defeat Assad’s tanks, helicopters and fighter jets".

Mind the caveats here: he stopped short of saying the US would directly arm the Syrian opposition, and didn't say how he would prevent the "Afghanistan problem" of weapons falling into the hands of groups that would later use them against the US.

Romney's criticism of the president for not trying harder to overthrow Assad also jars with his own condemnation, just a year ago, of Obama for being too aggressive in helping to overthrow another dictator: Muammar Gaddafi.

At the time, Romney claimed that US involvement in Libya was "another example of mission creep" and agreed with former US ambassador to the UN John Bolton that Obama has set himself up for "massive strategic failure". Unsurprisingly, there was no reprisal of this theme in this week's speech.

2) Arab spring: he'd support 'friends'

Romney issued a stirring call to US leadership, saying events in the Middle East were a battle "between liberty and tyranny, justice and oppression, hope and despair". He somewhat confusingly promised to both "support friends across the Middle East who share our values" and to stand with voices for freedom: "friends who are fighting for their own futures against the very same violent extremists, and evil tyrants, and angry mobs who seek to harm us."

As the libertarian Cato Institute's Justin Logan pointedly asks, "But which side was, say Egypt's Hosni Mubarak on, and which was the Muslim Brotherhood?"

3) Israel/Palestine: A two-state solution. Maybe

Romney said he'd commit to working towards "a democratic, prosperous Palestinian state living side by side in peace and security with the Jewish state of Israel." Of course, Obama and every other US president in the past three decades has supported the so-called "two-state solution," and Romney didn't spell out how he'd succeed in overcoming the deep-rooted obstacles that have stymied his predecessors.

Also left unaddressed was Romney's recently leaked fundraiser speech in which he despaired of any solution to the impasse. His proposal: "We kick the ball down the field and hope that ultimately, somehow, something will happen and resolve it." He also dismissed the Palestinians as "not wanting to see peace anyway."

On top of that, his personal closeness to hawkish Israeli prime minister Benjamin Netanyahu raises serious concerns about whether he'd be an honest broker on this issue, and the one below.

4) Iran: tough talk

Romney also talked tough on Iran, vowing, "I will put the leaders of Iran on notice that the United States and our friends and allies will prevent them from acquiring nuclear weapons capability." He added that he'd further tighten the economic sanctions the US and its allies are using to pressure Tehran over its nuclear programme. Neither of these represents a change from existing US policy.

Left unsaid was whether he'd support Israel's drumbeat for bombing Iran's nuclear facilities, although many expect a more hawkish line from him. Neither did he acknowledge that Iranians were rioting in the streets thanks to a currency crisis sparked by Obama-led sanctions, or indeed any of the evidence suggesting that the sanctions may be harming the Iranian people more than the regime.

5) Russia is our 'number one foe'

Russia got just a brief mention, when Romney said the president has "failed to lead" in Europe, "where Putin’s Russia casts a long shadow over young democracies, and where our oldest allies have been told we are 'pivoting' away from them." Note that Romney has in the past called Russia the US's "number one geopolitical foe."

6) China

China got just a sentence fragment in Romney's speech, when he again accused Obama of failing to lead "in Asia and across the Pacific, where China’s recent assertiveness is sending chills through the region."

The Republican candidate didn't say what he'd do to demonstrate "leadership" in Asia. But his words in recent months tell us something. In an op-ed piece in the Wall Street Journal in February entitled, How I'll respond to China's rising power, Romney slammed Obama's "weakness" and said he'd stand up to Chinese economic "abuses." He said on his first day in office, he'd designate China as a currency manipulator and take "appropriate counteraction." He also pledged to boost military spending to counter Chinese defence growth, and to confront the Chinese government on its suppression of human rights and free speech, without allowing trade or financial considerations to interfere.

7) The elephant in the room

Remember climate change? It didn't warrant a mention in Romney's speech, but with America still one of the world's largest polluters, it certainly matters to the rest of the world. In a nutshell, Romney’s climate change policy is simple: let’s not think about it. His position on whether global warming is real and whether humans are causing it has shifted several times, but he pretty consistently feels the government shouldn’t do much about it.

That said, the sad truth is that any president can do only so much about climate change if Congress fails to act. Obama famously said in his 2008 nomination speech that his election would mark “the moment when the rise of the oceans began to slow and our planet began to heal.” But while he has successfully raised fuel efficiency standards for automobiles and promoted renewable energy, his landmark cap and trade bill to cap greenhouse gases was killed in the Senate.

In foreign policy, the practical differences between what Romney or Obama can or will achieve are often overplayed. Despite being the leader of the most powerful country in the world, any US president's hands are tied in all kinds of ways.

Still, James Lindsay of the Council on Foreign Relations's analysis seems spot on. “If Romney has a foreign policy strategy, he still has not told us what it is," he told Politico. "The governor is very fond of saying hope is not a strategy, but that cuts both ways. He didn’t answer two key questions: what he would do differently and why we should expect what he would do to work.”

What do you think? Does the world want "more American leadership"? Does it need another "American century"? Watch the speech in full, and let us know how Romney's approach to dealing with the rest of the world sounds to you:

Sources: Washington Post, CBS News, Forbes, Move On, New York Times, Global Post, Politico, Foreign Policy, BBC, Avaaz, Mother Jones, Whitehouse.gov, Huffington Post, Wall Street Journal