The movie basically questions why Supes does what he does and the sacrifice he has to make to do it. I'm kind of looking at this as Superman I and II being one movie as Donner filmed both (or about 70% of part 2) at the same time.
Superman was being his Super self and all that but as the movie went on, we started to see that Superman has his own desires and feelings which kind of run contrary to his "position" as the world's greatest superhero (this was touched upon again in Superman Returns). He eventually gives it all up to be with the one person who he loves because he could never do so as Superman. That sub-plot in and of itself is questioning the superhero secret identity and what future lives these super people can actually live long before it became fashionable to do so. The movie is basically saying this guy isn't perfect.
Granted the movie did this all on the back of a romance but the issues the movie raised about a Superman and what it means to be Superman is still there. The movies don't necessarily question Superman's place in the world (somethings Snyder is trying but as I said very heavy handedly) as much as what it actually means to be Superman (if that makes any sense).