In Europe, where more than 200,000 people thronged a Berlin rally in 2008 to hear Barack Obama speak, there's disappointment that he hasn't kept his promise to close the military prison at Guantanamo Bay, and perceptions that he's shunting blame for the financial crisis across the Atlantic.
In Mogadishu, a former teacher wishes he had sent more economic assistance and fewer armed drones to fix Somalia's problems. And many in the Middle East wonder what became of Obama's vow, in a landmark 2009 speech at the University of Cairo, to forge a closer relationship with the Muslim world.
Obama's rock-star-like reception at Berlin's Victory Column in the summer of 2008 was a high point of a wildly successful European campaign tour. The thawing of a harsh anti-Americanism that had thrived in Europe was as much a reaction to the George W. Bush years as it was an embrace of the presidential hopeful.
Those high European expectations have turned into disappointment, largely because of the continued US military presence in Iraq and Afghanistan and Obama's failure to close Guantanamo Bay in the face of vehement congressional opposition.
Foreign policy expert Josef Braml, who analyzes the US for the German Council on Foreign Relations, said many Germans give Obama too much of the blame because they don't understand the limits of his powers.
"There's a lack of understanding both of how the system of checks and balances works - or doesn't work any longer - and a lack of understanding of how big the socio-economic problems in the United States are, which cause the gridlock," Braml said in a telephone call from Greece, where he was on vacation.
Blaming Europeans for crisis
Obama's views on Europe's financial crisis also have rankled some on the continent. In September, he said the crisis was "scaring the world" and that steps taken by European nations to stem the eurozone debt problem "haven't been as quick as they need to be."
The Obama administration describes the eurozone crisis as a European problem that needs a European solution. The US and Canada last month refused to participate in boosting the International Monetary Fund's financial resources to manage the crisis.
"I think people see through his game to put the blame on Europeans - I think Germans and Europeans still know where the economic crisis had its beginning," Braml said. "That's just finger-pointing, not doing a fair analysis of the dire situation in the US, but I can understand Obama is doing that because he wants to get re-elected so they need to shift blame around on the Republicans or the Europeans."
Mehmet Yegin, a specialist in Turkish-American relations at USAK, the Ankara-based International Strategic Research Organization, said Europe still sees Obama as superior to Romney, "because they primarily evaluate Romney as a Republican and their memories about George W. Bush linger."
Many in the Mideast also would like to see Obama win a second term, though they feel he has not lived up to his Cairo speech, in which he extended a hand to the Islamic world by calling for an end to the cycle of suspicion and discord.
Obama has been the US president "least involved in the Palestinian issue," said Mohammed Ishtayeh, an aide to Palestinian President Mahmoud Abbas.
"We were very optimistic when Obama was elected. He talked in his meeting with us without looking into his notes; that tells how much he knows about our issue," he said.
But since Obama made his Cairo speech, Ishtayeh added, "he found his hands tied and couldn't make much progress."
Obama also has a strained relationship with Israel, where Bush was popular. Obama and Israeli Prime Minister Benjamin Netanyahu have been cool to one another in their handful of meetings. Obama's Mideast envoy, former US Sen. George Mitchell, made no progress during two years of frequent meetings with both sides before quitting last year.
Despite the chilly relations between Obama and Netanyahu, overall ties between the allies remain strong. The US has backed Israel on several key occasions at the United Nations, for instance, helping block a Palestinian attempt to join the world body last year without a peace deal and fending off attempts by other countries to charge Israel with human rights abuses.
"Concerning Israel, he has proved that he is not absolutely rigid but is willing to reconsider when confronted with facts that he would not have expected," said Avraham Diskin, a political scientist at Jerusalem's Hebrew University.
"He began very inexperienced on all fronts, but he is a very intelligent person and Israelis see that," Diskin added.
'Obama ignores Kurds'
In Iraq, site of the war that fed much of the international community's dislike of Bush, Obama has received some credit for pulling out combat forces last year.
"President Obama has removed so much of the cowboy image of America that has been imprinted in the mentality of Iraqis by Bush," Baghdad lawyer Raad Mehsin said.
But Carawan Ahmed, a high school teacher in Iraq's northern Kurdish capital of Irbil, said Obama has ignored the Kurdish minority, which continues to struggle against the Shiite-dominated government.
"When Democrats, including Obama, are in power, we lose the sympathy and support from America. To be frank, the Republicans protected the Kurdish people, while Obama's administration is not," Ahmed said.
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