We like the mining robot Dave because he feels bad about being a screw-up, and we identify with that. That is, in some ways, Cutie and Dave are in similar positions: they're both robots in charge of other robots. But Cutie purposely "rebels" against orders because he thinks he's following a higher order (and he actually is, since he's following the First Law); whereas Dave is accidentally failing to fulfill his mission and just feels terrible about it. Like, when Powell and Donovan ask him why he's not producing a lot of ore (he's a mining robot, after all), Dave tells them:
I can't explain that, boss. It's been giving me a case of nerves. (30)
So that's Dave: a robot with a case of nerves.
Actually, Dave is a strange case in this book because his problem turns out to have nothing to do with the Three Laws of Robotics. (Check out the other cases that Powell and Donovan get into: Speedy, Cutie, Brain—they all have issues with the Three Laws.) Dave's issue has something to do with the fact that he's in charge of other robots. In other words, all the other robots in this book have issues with humans—Dave is the only robot who only has issues with robots.
Of course, we don't know that at first. In fact, Donovan first suspects that Dave might be planning a robot rebellion (50). So maybe Dave is in this collection to remind us that even people who work with robots all day might worry about the typical sci-fi stories about rebellion.
What does this robot tell us about robots? Dave certainly reminds us how human these robots can be—that is, they have emotions as well as thoughts. And when Powell and Donovan test him, they not only give him math questions (which any calculator could do), but also test him on questions of ethics and judgment, which not even the newest iPad can do (38). So Dave reminds us that robots are emotional and ethical. And Dave does give Donovan a chance to talk about robot rebellion, which is, of course, not the answer, because robots are very ethical.