1.) MacArthur was ordered to leave the Philippines, and in doing so, he left a bunch of men behind to die/get captured by the Japanese. This rankled people (granted, it was under orders), and then he was given the Medal of Honor afterwards. It became more of an issue once the nation learned about the Bataan Death March and the treatment of those left behind. (Personal note: I went to Wainwright Elementary School, named for General Wainwright, who was a POW, and who shared in his men's plight. He was found severely malnourished, and MacArthur had opposed his Medal of Honor in 1942 because he felt Corregidor should not have been surrendered.)
2.) In Korea, he openly suggested open war with China, and a Republican congressman read a letter aloud on the House floor from him: "It seems strangely difficult for some to realize that here in Asia is where the Communist conspirators have elected to make their play for global conquest, and that we have joined the issue thus raised on the battlefield; that here we fight Europe's war with arms while the diplomats there still fight it with words; that if we lose the war to communism in Asia the fall of Europe is inevitable, win it and Europe most probably would avoid war and yet preserve freedom. As you pointed out, we must win. There is no substitute for victory."
This directly undermined the president, and he was caught doing this to Congress, in the Press, and to our foreign allies.
That said, he was very popular. In retaking the Philippines, he placed humanitarian concerns over military concerns (limiting airstrikes in Manilla, did not restrict road usage for people fleeing fighting), and did an excellent job. He was a very effective military governor of Japan, working quickly to alleviate famine. His loss in '41/42 was probably unpreventable given what he had at hand to resist the Japanese invasion. The invasion at Inchon in the Korean War overcame a lot of logistical issues, and was a wild success, but he initially vastly underestimated the extent of the Chinese reinforcements that pushed the US back deep into South Korea (but so did many others).
Personally, I would say he was a decent general, whose reputation definitely outpaced his actual achievements. He was definitely a proud individual, and this led to his attempt to undermine President Truman, which led to his dismissal.
History has not been kind to his reputation, especially as it became clear that he accepted half a million dollars from the Philippine president as he retreated, and that he undermined the President to allied diplomats (which Truman knew, but did not release to the public).
He's a bit controversial in Australia. Australian historian Peter Brune has discussed it in a number of his books which usually concentrate on the war in New Guinea.
One was that MacArthur made sure that Australians weren't in any real planning positions even though Australians made up a majority of his force for quite a long time in the Pacific and also were more experienced since they'd recently conducted warfare against both the Germans and the Italians in North Africa. The claim is made that MacArthur liked to surround himself with Yes Men. He couldn't stand anyone who didn't think everything he did was brilliant. It meant that there was no one around to tell him when he was wrong.
Another was that he lead from the extreme rear. His HQ for a time was in Melbourne (bottom of the Australian mainland) and then was moved to Brisbane (still thousands of kms from the front lines in New Guinea). MacArthur created an image of himself though that he lead from the front such as when he travelled to New Guinea and gave the impression to the media (which he always made sure were around........ he basically had his own press corp) that he had personally being leading the Allied forces at the front even though he'd been no where near the fighting.
He ignored Australian intelligence which turned out to be quite good. This meant that time and time again Allied forces in New Guinea were under the assumption that they were fighting a lot fewer Japanese troops than they were. When reports from the front came back stating that there were more Japanese forces than thought MacArthur would still continue to ignore it because it contradicted his intelligence. All along the Kokoda Track he kept belittling the Australian forces to their commanders because his intel said that they outnumbered the Japanese forces and it was shameful that they were being pushed back by such a small force. This just wasn't true in the slightest.
At Gona he ordered the Australian forces to attack without mounting recon of the Japanese positions (this caused them to attack through a swamp against prepared Japanese defences such as bunkers) and then when the Australians there disobeyed his orders, mounted recon, found a way around the Japanese defences and took Gona MacArthur told the media that it had been his insistence on recon that had won the day.
In the media he portrayed victories as American and defeats as Allied no matter the disposition of the forces involved.
Sources by Peter Brune
A Bastard of a Place
We Band of Brothers
Those Ragged Bloody Heroes
The Spell Broken
Edit - Added a bit about Kokoda.
Short answer? He's terribly overrated.
Long answer: While the fall of the Philippines in 1941 was a forgone conclusion, McArthur's own actions went a long way to making the defense less effective than it should have been. Quite simply, he was overconfident; and this overconfidence resulted in the destruction of much of the military aircraft in the Philippines due to a Japanese attack and left the US and Philippine Army forces deprived of air support.
Worse was his attempt to defend the whole of the Philippines, which was basically impossible given that we have over 7,000 islands and more coastline than France. The Japanese were thus able to land mostly unopposed with a superior force; forcing McArthur to withdraw into the Bataan peninsula.
Now, to be fair, the defense of Bataan itself proved to be rather successful. However, the withdrawal itself was a barely averted disaster. Quite simply some of the best units of the Philippine Army had to be used up to cover the rest of the army's retreat. Moreover, a lack of preparations meant that the troops immediately had to go on half rations in Bataan due to a lack of supplies - whereas the Japanese easily captured all the stockpiled supplies in Manila.
Hence, had McArthur not attempted to defend the whole country and organized a withdrawal into Bataan from the start, it's conceivable the garrison there could have held out for much longer than it did.
McArthur's real skill was demonstrated when he was on the offensive and in command of an amphibious force. He understood how a well-placed landing in the enemy's rear areas could disrupt and unhinge his entire position; and he demonstrated this during the New Guinea campaign in World War 2 and at Inchon in the Korean War.
The problem is that this only fed into his already towering ego - which led to many quarrels with the Navy (who carried the troops and should be credited for figuring out how to logistically execute McArthur's often over ambitious schemes to begin with) and his superior officers; particularly when he tried to deflect blame for his own failings. This is the reason why his career was ended - after the UN forces faced disaster and annihilation in the Korean War due to the Chinese intervention (which happened in large part due to McAthur's over-confidence), McArthur tried to point the finger at President Harry Truman and advocated the use of nuclear weapons. This was clearly unacceptable in a democracy.