Why so bad? The second man on the list of "bad presidents with a good side" was the oldest son of the first. Like his father, he served a single term as president, managed to be hated by his opponents while getting only half-hearted support from his own political allies, and was probably secretly relieved when he was defeated in the next election and thus got an excuse to walk away from an office that had pretty much become a living nightmare for him. Unlike his father, he became the first man to win a presidential election even though he came in 2nd to Andrew Jackson in both the popular vote and the electoral college. He managed this because the election of 1824 was a complicated 4-way race in which no candidate got more than 50% of either the popular or electoral vote. As per the United States Constitution, the election then decided by a vote in the House of Representatives. In the House of Representatives, the 4th-place candidate, Henry Clay, encouraged his supporters to vote for Adams rather than Jackson, which guaranteed a victory for Adams. Soon after, Adams appointed Clay as his Secretary of State. This looked like a painfully obvious case of Clay selling the votes of his supporters in return for becoming the senior member of the new president's cabinet. Jackson's supporters immediately accused Adams and Clay of reaching a "corrupt bargain" to thwart the will of the voters, and this accusation tainted John Quincy Adams badly even before he was sworn in as president. Jackson and his supporters used it again and again for the next 4 years, and amazingly Adams never even publicly disputed or denied it. Unlike his father, John Quincy Adams didn't end up having any significant accomplishments of his own as president, positive or negative. He did, however, mimic his father's inability to work well with others, including even Henry Clay, who might have been expected to be a close ally since they were both under attack for the same reason.
In his defence (sort of) ... John Quincy Adams really was a bad president, in the sense of being ineffective and accomplishing little, but this was not because he was corrupt. On the contrary, he was too rigid in his principles to be effective. Remember the old saying that "the apple doesn't fall far from the tree"? John Quincy Adams was very different from his father in some ways, but he matched and even exceeded Dad in his determination to do what he thought was right, regardless of political realities or consequences. There is no evidence that there was any "corrupt bargain" between Adams and Clay in 1824. Clay and Adams agreed with each other on more issues than either of them agreed with Jackson, so it was no surprise that Clay ended up supporting Adams when the election came to the House of Representatives. Adams had worked with Clay in a diplomatic role before when both of them were on the team of American diplomats who negotiated the treaty with Great Britain that ended the War of 1812, and he considered him a capable negotiator who could make a good Secretary of State.
Why didn't Adams even defend himself against the charges that made much of the country question the legitimacy of his presidency? He apparently considered it beneath his dignity to answer the charges. This might sound bizarre and unbelievable to many people today, but it actually fit well with Adams' personality. John Adams Sr. had been stubborn, but also had a down-to-earth streak and did not hesitate to let people know exactly what he thought. John Quincy Adams, on the other hand, had the hypersensitive sense of "personal dignity" of both an elite gentleman and an opinionated intellectual, and often responded to criticism by silence that was meant to show that the accusations of his opponents were not even worth responding to. Unfortunately, that approach is almost never successful in politics. American politics had become more populist, more aimed at the "common man", since his father's time, but John Quincy Adams had moved in the opposite direction. He was successful in almost every other office that he held - as an assistant to US ambassadors in Europe and then an ambassador himself, as Secretary of State (the "Monroe Doctrine" was actually mainly his creation"), and after his presidency as a long-serving Congressman from Massachusetts, where for several years he was virtually the only elected official in the national government to openly criticize slavery while also advocating government funding of scientific research, which most politicians of the time considered to be outside the government's responsibility.
When it came to presidency, however, he was almost comically mismatched. He was probably painfully aware of this for most of his presidency, but he followed his own rigid sense of personal behavior and never said anything about this.