It wasn't so much he changed the script, but Singer has a tendency to come up with spontaneous ideas on set, and then shoot them...kinda' like a fanboy. "Hey...wouldn't it be cool if we had a flashback to Superman as a kid jumping through the cornfields? We're already out here shooting his return. Hey, producer, figure out how we can do that!" Two days later, they're shooting that in an improvised schedule. (I'm not saying that's how that scene came to be, just an example.) As he does that more and more, and he falls in love with his ideas, the original theme of the picture begins to be lost. It worked for him in the past, X2 is a fantastic film, but it is the source of some of the casts displeasure with the working experience, most notably Halle Berry's.
The original theme of Superman Returns, which was contained much more in the script, was how would a world who was used to Superman react to his disappearance and how would that world resent him when he returned? This was shown in a macrocosm and in microcosm through Lois. You can still see this in tiny bits and pieces throughout the film, but it is diluted and pretty much lost in all the film's digressions. I don't know for sure exactly what scenes are Singer's indulgences, but I predict most of them are Luthor bits, small action beats, and mostly the overt Donner nostalgia.