Many Americans felt that the result of the 1824 election was fraudulent primarily due to points 2 and 4 from your list:
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No Majority in the Electoral College: Andrew Jackson received the most electoral votes but did not secure a majority, which triggered the decision to be made by the House of Representatives. This was a significant point of contention because the House was choosing from the top three candidates, excluding the candidate with the most electoral votes (Jackson). This process raised questions about fairness and perceived legitimacy.
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Henry Clay's Influence: As Speaker of the House, Henry Clay's support was crucial in the election of John Quincy Adams. After Adams was chosen as president, he appointed Clay as Secretary of State. Many viewed this as a "corrupt bargain," suggesting that there was a backroom deal between Clay and Adams. This perception of collusion further fueled the belief that the election was unfair or illegitimate.
While point 3 is also relevant—Jackson received more popular votes than Adams but lost the presidency—it was the context of the decision-making process in the House and the subsequent appointment of Clay that led to widespread accusations of corruption and fraud. Therefore, points 2 and 4 are chief among the reasons behind the sentiments of fraud surrounding the election outcome.