Briefly, Ross puts forth a non-absolutist theory revolving around prima fascia duties that are permanent but not always decisive. Those duties are fidelity, reparation, gratitude, justice, beneficence, non-maleficence, and self-improvement. He admits that this is not an exhaustive list, but each is necessary. In particular scenarios, some duties may be outweighed by others but they are always important regardless.
Shafer-Landau points out three primary difficulties with Ross's theory: 1. Arbitrariness: there's no apparent reason for why these particular duties are included. 2. Balancing: it's not clear why some duties take priority in certain cases, if they are not ranked. 3. how do we come to know these duties and the final duty to act on in specific cases?
While I think these are certainly good to point out, I personally don't think they're true objections. Each of them can simply be deduced to intuition. When you really think about it, why do we do anything? Regardless of what might be truly behind our actions, we do things because something (whatever that may be) compels us to do so. There are many days when I don't feel like going to work, but I still go. If I didn't find any compelling reason to go--even though I say I don't "want" to--I wouldn't. I think what we're discussing here is similar.
Presumably, Ross included these prima fascie duties because that's what his intuition instructed him to include. The only reason that we see this as a "difficulty" is because it's not as satisfying as we'd ideally like it to be. We dislike admitting that some things may happen by chance for the same reason--as human beings, "by chance" and "intuition" aren't satisfying answers, even if we make the majority of our decisions based on intuition. That's the reason that I decided to go to work even when I didn't feel like it, whereas my roommate often calls into work when she doesn't feel like going. We're wired differently; our decision-making is necessarily affected by our individual intuitions and dispositions. So while appealing to our intuitions might not be as ideal as a solid, empirical explanation, morality is not a science.
It would, of course, be nice if Ross's theory gave us a methodical way to calculate the absolute moral decision in every case. But given the complexity of the world, ourselves, and the decisions we face, is that even a feasible demand? I would argue that it absolutely is not--that when you really think about it, it's almost silly to ask. Utilitarianism is an interesting and thought-provoking theory, but the fact of the matter is that very little of that is actually going through my head when I'm contemplating a moral decision. I might be thinking about whether or not it will hurt or help others, but I'm not calculating hedons in my head. (Nevermind that I don't even know what that would look like in practice.)
I think Ross is onto something here. By focusing on what actually goes through our heads when we're making a moral decision and considering the complexities we face, he's conjured up something that actually seems to make sense in the real world as it really works, even if it hasn't allowed us to "close the book" on our discussion of morality.