I don't know that anyone can give you a full answer to this, as it's quite a subjective answer, unless you just want instances of things he did that might be inconsistent with popular knowledge, like affairs and domestic abuse.

If you're looking for an answer to "What was he really like?", then I would suggest that you look to autobiographies of those who worked closely with him, or near him.

When I was reading a biography of Septima Clarke, a teacher in the South who helped set up schools to educate African Americans and get them enrolled to vote, I found that she had views of Dr. King that weren't consistent with the dominant history of the Civil Rights Movement, or what Julian Bond called 'The Master Narrative'.

Here's what I wrote in my essay, and I've dropped the sources below:

 

The Highlander schools shared the same philosophy as clubwomen in the South: that leadership was not being “the head of an organisation” but rather, was centred on “assuming the responsibility to get others involved.”^1

In ‘Ready From Within’, Clark mentions that she didn’t think King had a high opinion of women, and that when she suggested the concept of creating other leaders within the community, such as the Highland school advocated, it was seen as “looking down on Dr. King” because she had suggested that someone else lead.^2

“...you don’t have a right to speak. You can work behind the scenes all you want. That’s all right. But don’t come forth and try to lead.”^3

 

The third quote is Septima Clark's paraphrasing of someone in the movement, not Dr. King himself. The exchanges show that within the upper circles of the movement, there was definitely a sense of elitism in some quarters. Dr King isn't implicated in these, but it does suggest he was somewhat removed from the grassroots campaigners. It's important to note that these were people who had been campaigning for the last fifty years, yet the people surrounding Dr. King were contriving to have him as the only recognisable leader of the movement.

If you want more information, as I said before, I highly recommend autobiographies or biographies cowritten with the subject. They will be inherently biased: people have strong opinions of others, and even years after the fact will be staunch supporters or opponents. They will also attempt to manipulate people to share their own views of the man.

 

^1 Debating the Civil Rights Movement, 1945-1968, edited by Steven F. Lawson and Charles Payne, p.109.

^2 Ready From Within: Septima Clark and the Civil Rights Movement, by Cynthia Stokes Brown, p.78.

^3 see Note 2.