I think his biggest mistake wa meeting young Tom Riddle. Tom clearly nothing but evil at that time, and had absolutely no guilt or hesitation to insult, bully or even kill anyone even as a young kid. The orphans were clearly trying to avoid him, which Dumbledore thought was because Tom couldn't control his magic at the time, that I had to say, the most unrelatble thoughts for a wise wizard like him. The moment Dumbledore introduced Tom to magic, the young boy demanded to know more rudely. After Dumbledore considered regret making his decision and leave, Tom pleaded softly and said, "I can talk to snakes too. Is that normal?"

Dumbledore thought for a moment, and decided to go on. I think this was his most stupid mistakes of all centuries. He could have just claimed himself to be a magician and that magic isn't real and run Scot free, but no. He just had to give him more information to let Tom kill Dumbledore in the future.

Although I think it would be better if Tom was a simple kid who didn't believe magic even though he had magic, so that he would have never turned to Voldemort, killed Lily and James so that Harry would have a happy wizarding life as Dumbledore die of old age, I think if Dumbledore hadn't turn back to tell young Tom Riddle more, there would never be The Boy Who Lived.

I don't like Dumbledore and I think that he was responsible for most of the deaths I mean it's really weird that he always arrived on exact moment and mostly late tbh.

He was great teacher we can't deny that, he was inspiring he was fair and he was brave and gentle too.

We all know that he was offered the post of minister of magic atleast 3 times but he refused because he knew that power doesn't suit him.

And he has bad experiences in past when he wanted power. Like the one with Grindelwald and all of that but finally he was the one to defeat Grindelwald.

He was a natural leader and maybe a git who only cared about his knowledge like said by Aberforth.

Dumbledore sorta always knew what's happening in Hogwarts and outside Hogwarts too maybe because he had too many contacts like Mundungus and many more people like him whom Dumbledore had maybe helped once so they were loyal to him. Just like Hagrid.

And as said by Remus Lupin that Dumbledore gives people second chance even if they don't deserve it.

And he was kinda referring to Snape at that time.

Three mistakes Dumbledore made

1

He didn't saved or even tried to save Sirius.

Well actually it can't be a mistake because he knew if Sirius is there he would never let Harry live with the Dursleys so Lily's protection can't work and it can be easy for deatheaters to find and kill both of them.

And maybe he himself didn't know that Sirius switched places with Peter. But it's just my theory so it can be his mistake too.

2

Like I said above he always arrive precisely on time or sometimes a bit late if he already knew about everything so he can just hurry and he can avoid too many fatalities.

But maybe it was all part of the plan and maybe since Snape was on his side he told Dumbledore that Lucius and other deatheaters are going after the prophecy.

3

Now this one is said by himself that it was his mistake that he should have give Harry occlumency lessons instead of letting Snape do it because he knew that Harry and Snape don't get along well but we can't deny he had important stuff to do at that time like figuring out about Voldemort's past and where his horcruxes can be.

4

I know you only asked for three but I have a forth one too sorry about that.

So the fourth is that he shouldn't have let Grindelwald's idea take over his mind. I can understand that he was angry that his talent was being wasted and like Aberforth said there's no awards for looking after your mad sister who try to blow up the house every other day but I think Grindelwald had a great influence over him and they both were almost equal so they get along well but atleast Dumbledore realised what they're doing or will do was wrong and stopped.

I don't want to justify anything because everything happened for a reason we can't deny that and none of us wants to change the story.

When Dumbledore called Voldemort Tom when he came after years to claim the post of DADA teacher as offered to him by Armando Dippet and Voldemort was angry at that time and more than that he didn't expected Dumbledore to know about him too much but bad for him Dumbledore already knew too much.

And the second one is my favourite when Fudge came to arrest him and he overpowered Fudge, Umbridge and two of the best Aurors well one of them was just acting but still we can't deny Dumbledore has got style. 😉