Personally my problem with Superman being out of character in the film had nothing to do with his relationship with Lois. Granted, I didn't like some of the choices he made (especially the 'See ya round

' kind of departure at the end having just gone to see his son!), but I also often don't like some of the mistakes he makes in the comics. What defines him as the greatest superhero is how he deals with his mistakes, and in this film he dealt with them badly.
But as I said, that's not my main problem - maybe there is a multi-movie story thread in which he handles these in a heroic (and therefore fundamentally 'Superman' way) later on. But that's really just the problem. He's supposed to be the greatest hero of them all, and in SR he wasn't heroic at all. Using superpowers to save people isn't heroic: after all, he has superpowers. The only really heroic thing he did was lifting NK out of the sea, because of all the kryptonite. But that's not enough. His demeanour and attitude were all wrong. He came across as shy and nervous, and that's not right for Superman. Granted, he's going to be a little disoriented after his five year absence, and a bit taken aback by the circumstances he is greeted with when he gets back, but I would have thought that his shyness and nervousness would be fleeting, to be replaced by his strong confidence that inspires leadership, that we have all come to expect from Superman, after a very short space of time. That's what makes leaders; they are always just as scared or uncertain as everyone else, but they provide an image and persona of strength and integrity that causes others to trust them and follow them, and that is what was missing from this depiction of Superman.
On top of that, the story was weak, uninspired, and badly told. Singer has lost the dramatic flare and penchant for tension building that he used to be so good at. They were lacking from the first two X-Men films and they were lacking from SR.