Its why his enemy in this one is Zod.
Supes isn't invulnerable. He is really, ridiculously tough, but he can be beaten by sheer, brute force. Doomsday proved that. Zod has the same powers he does, after all, and is a much better trained fighter - having been able to fight before he was given his abilities.
Superman's ridiculous level of ability does, however, mean that the only way to believably beat him is to have someone come in stronger than he is - and there aren't too many of those. It does make it hard to make a believable villain, in the end, that he can go against.
However, one of the best examples of why Superman gets beaten or momentarily foiled by weaker, but more devious opponents was summed up well in the 'World of Cardboard' speech where he beats the holy hell out of Darkseid in a Justice League movie. Superman straight up exults that there is finally someone he can go all out on, because he knows Darkseid can take it. He gives him an absolute hiding. But it illuminates one of the things about Superman which make him, in my eyes, a bit more endearing - just because he does have these incredible abilities, he doesn't overuse them - in fact, he makes a habit of always using just enough of them. Its probably ingrained in him. He knows exactly how much harm and damage he can cause if he goes full gear, and its the Clark Kent in him - the shy, awkward, and nervous reporter who can't tell the girl he loves how he feels - that holds back the living god who fights back against unimaginable powers of destruction not because he can, but because he feels he must. But he restrains himself, because the more he does that, the less removed he becomes from the humanity he identifies himself with so strongly - and because he wants people to identify with him, and his humanity, rather than his omnipotence. Responsibility and living up to what people believe he should be is the overwhelming driving force in his existence, but being the last of his kind (nominally) means he is also lonely - so he tries to blend in. Because when you think about it, in truth, he has no reason to take on the Clark Kent persona, at all. He can exist as Superman 24 hours a day if he wants, who will argue with him? But he does, so he can be more human.
Its the character of Superman that I like, the burden he chose to take upon himself, which is enormous. Its easy to see the godlike figure and believe it is easy for him, but the human side of him - the actual character part, not the abilities and powers part - is the one doomed to an existence of heartache, battle and perpetual solitude, but he does it anyway - because that is what heroes, in his eyes, are supposed to do. A movie about him finally taking on that vast, unending responsibility, knowing exactly what it will cost him and how hard it is going to be, is hopefully what I will see in this film - and I'm looking forward to it.