What I'm about to say probably has already been said and more than once in this thread, but since the OP asked, I can't help myself.
Before I dig in I will say that I re-watched Superman Returns after watching Man of Steel and now I don't loathe SR as much as I once did. I think SR was harder for me to swallow when it served as the 'final' Superman movie, the bookend of the Reeve era films. But now that I have something else to compare it to, I've actually found some nice things to say about it.
I liked the relatively brighter color scheme of SR, the John Williams score, the maintenance of the Donner aesthetic for Krypton, and the flying effects all better than what I saw in MOS. I also liked the inclusion of the George Reeves-era actors. SR was more of an homage (not always in a good way) of the Reeve era but also acknowledged George Reeves contributions. After reading a Superman biography recently I appreciated that more. I can't think of an action scene in MOS that was as well shot as the plane rescue early on in SR.
Now the rest...
Singer made a mistake in connecting the film to the Donner films with totally different actors. I can get some call backs and using the Williams music and even the aesthetic, but it was a mistake not to at least make the characters his own and to update the Superman story for the 21st century. For an example of what I'm talking about, I take Smallville which sparingly used some Donner-era stuff but largely charted its own course. SR could've done something similar.
Singer was mistaken to think that general audiences were as taken with the Reeve films as diehards like me and would remember or care about the intricacies of Superman 2 and be willing to ignore Superman 3 and 4.
To be fair to Singer he did try to make Superman relevant but I felt he was a little too heavy with the religious metaphor. I also didn't need Superman to be an absentee father. Perhaps Singer was going for an emotional core with the film, but the actors he had didn't quite pull that off.
SR was too drab, too somber, if not in subject in tone and execution. Superman wasn't super enough (except for the plane rescue). The film was lacking in action. And the one time Singer let Superman do an amazing feat with the lifting of the Kryptonite-laced island it was an impossible one for Superman.
Lex's plan didn't make much sense. Who would want to live on a barren Kryptonite island? Lex's crew was boring, including Parker Posey. They were too small bore for a guy like Lex, or rather the Lex many people had become accustomed since the mid-80s.
The casting was a mixed bag. I can't blame Routh because I think he got bad direction. Kate Bosworth was a wet noodle. She was too young, or looked too young to be playing a Lois after Superman 2 (or 3 and 4, whatever), and her take on the character was way too sedate. Spacey was an inspired choice for Luthor, but he got saddled by the story. I can only imagine what could have been if Spacey had been allowed to reinterpret the character in a new story.
It sucks when Richard White comes across as more heroic than Superman. And the less I say about the kid the better.