The endings of adoptions
Author correctly points out the elephant in the room for sources of unsatisfying endings with unresolved mysteries: adoptions of ongoing manga series (or any ongoing series, since there are adoptions of light novels too). The honest answer to his question is that I didn't think of it; I was more or less only focusing on things that were within the control of the anime creators.
Having said that, it's still the anime studio's responsibility to solve the problem. I can only think of two good approaches; the studio can break with the manga and come up with their own answers to the mysteries (call this the Full Metal Alchemist approach), or they can do their best to push the unanswerable mysteries into the background and focus the story on something that they can resolve (call this the Fruits Basket approach).
Both approaches can produce satisfying endings if done well, but I think that only the first approach produces a work that stands alone and has a real conclusion. With the second approach, I think you pretty much always get 'and then life goes on, with more happening' endings; satisfying but not complete.
A thought on the problem of endings
One of the things that I've gotten used to as I watch anime is that many anime shows have unsatisfying endings. The show will go along decently or even great in the regular episodes, building up mysteries and intriguing events, and then they reach the concluding episodes and, well, people wind up sitting around going 'that's all? that was their explanation for everything?'
(This is so common that people have coined terms like 'Sunrise ending' and 'Gonzo ending' to summarize how certain studios always seem to end shows badly.)
In thinking about this I've come to an obvious realization; a good part of the problem is, to put it one way:
It is much easier to come up with intriguing mysteries than convincing explanations.
Anime loves throwing intriguing mysteries into its mix, I think partly because it's a simple way to build viewer interest, but over and over again it fails to come up with really convincing explanations to them. And while not everything has to be explained, the shows have generally put the mysteries in the foreground (it builds more interest) so they can't just leave them unanswered because that would make the ending equally unsatisfying in a different way.
(I don't think that this is just the writers writing themselves into a corner as the show goes on, because my vague impression is that most fixed-length anime is completely plotted out beforehand. I could be totally wrong about that, though.)
Naturally this strikes certain sorts of shows more than others, because you generally don't get peculiar mysteries in, say, romantic comedies. The more ordinary the show's setting is the better, at least for avoiding this particular problem. Going the other way, it's reached the point where I've started to actively expect to be disappointed by the answer to any mystery a show raises, which means that I generally expect shows that have a lot of central and important mysteries to wind up being not very good.