A Lack of Epistemological Awareness
One of the most important things that modern atheists can learn from David Hume is the limitations of sense perception and reason. That’s just something that they haven’t taken seriously at all. David Hume took it very seriously and saw that there’s really no way to rationally justify reason. Whether it’s deductive logic or inductive logic, you just can’t give an argument for it that doesn’t use it.
That was a little unsettling, but Hume was willing to simply say, "Look, that’s just the way it is." Today’s atheists simply don’t take it seriously enough and I think that has ramifications for other things they believe. They’re so willing to just accept something on faith: "I’m just going to trust sense experience. I’m just going to trust reason. Who wouldn't?" However, I think that’s just naive, because it shows that there’s this lack of epistemological awareness.
The Relativity of Moral Values
Another thing modern atheists could learn from David Hume would be that moral values really come down to the one doing the valuing—the valuer. There’s no value out there in the world; you need a person to have value. I think one of the things that today’s atheists try to do is try to argue for an objective morality. But I think that if they took Hume seriously, they would see that there can be no objective morality.
For example, what makes gold valuable? Well, we do. Right? Similarly, when judging an act of lying, who decides whether it's good or bad? Thumbs up or thumbs down? It depends. It’s up to you. There’s no standard out there.
Hume was very aware of this fact, and I think today’s atheists could learn a lot from just taking him seriously.