OK, so let's take it for granted that you, as a graduate student, have every reason to expect to get useful, instructive feedback from you instructors. Sadly, things don't always work out as they ought.
Is there anything you can do to improve your feedback? Of course there is.
One obvious route is to be a brown-noser, to use to colloquial and cynical expression of my youth.
But assuming that we don't want to sacrifice our dignity, is there anything we can do? Of course.
Asking nicely is a good place to start, but if you write a good cover letter, it can help a lot.
First of all, imagine that your professors really want to help you, but are extremely busy. For too many, perhaps, the former (their wanting to help) may require some active imagination, but the latter (their being busy) is probably pretty much true. Anyway, we start by imagining a helpful, busy audience to set the tone.
What do we want to do?
1. Don't waste time! Keep the cover letter to one page.
2. Request their attention, and acknowledge that they are probably busy.
3. Tell them what you're sending them.
4. Tell them what to focus on (if anything in particular), or tell them what kind of feedback you're looking for.
5. Be confident and assertive, while still being respectful, even deferential.
I think numbers 1, 4 and 5 are the most important: keep it short and sweet, clear and focused. If you tell them what to do, you make the task that much easier for them, and therefore they're that much more likely to do it. If you act confident, they'll be much less likely to look for problems. If you assert what you have improved and focus their attention to the new strengths, you're like to get more positive feedback.
To follow up on that last point, there is a corollary to point 5: Don't apologize for your work or direct attention to the weakest points if you have any concerns about getting problematic feedback. Making apologies and pointing out weaknesses is virtually begging for the reader to focus their attention on the worst parts.