Here's a summary of a largely Christian perspective:
Let's only consider the state of the world that God exists. God is perfect. That is, God attains to the highest standards that exist. If the world was created by a perfect God, then the world should be perfect. However, the world is not apparently perfect, which indicates a few alternatives, such as God is not perfect, or the world is perfect but it just appears to be imperfect, or even that the world fell from perfection independent from God.
The former doesn't seem likely since if the world is not perfect (because God is not perfect), and perfection is defined as the best possible standard, then that means there is a standard of perfection and God doesn't meet this standard. The standard of perfection would 'exist' and yet God who exists is not as perfect as the standard, so that seems inconsistent. In fact, one could argue that the standard of perfection is 'God' and the non-perfect being is a degenerative derivative of 'God'. Such inconsistency doesn't seem likely.
The second option - that the world is actually perfect despite the appearances - doesn't seem likely either. True, the world has many 'perfect' moments and there are times when the world seems perfect, but all too frequently we are reminded how imperfect the world is. Now, perhaps our standard is all messed up. Perhaps mayhem and other tragedies in nature are not part of the standard of perfection and are either undecided cases of perfection/imperfection, or meaningless cases having nothing to do with the perfection/imperfection classification. Maybe the standard of perfection has to do with the 'right' number of blackholes in the universe, and the universe has the right number of blackholes to qualify it as a perfect universe. Or, maybe the 'Matrix' solution is the ideal. In the movie the 'Matrix', human society was created perfect at first, but the humans awakened in the real world and would not stay sleeping and therefore continue to reside inside the Matrix. By making an imperfect world (modelled after the late 20th century), the machines were able to make a perfect world for them where humans acted as human batteries supplying their energy consumption needs. All of these 'solutions' are somewhat anti-intuitive. They cannot be ruled out, however if 'God' is grand enough to create a sophisticated universe to allow intelligent life to evolve, then it would seem that God has enough foresight and knowledge to understand human needs and human pain such that with a little more effort God could eliminate that pain and fulfill human needs without any extensive additions to the laws of physics. If God cannot foresee the pain and lack of fulfilled human needs, then it would seem that the standard of perfection that God runs the universe by is quite a bit less adequate than standards by which humans run their civilization. All in all, the whole idea of an evolved, primitive intelligence having an apparent standard of perfection higher than the Creator, seems anti-intuitive at best, and outright ridiculous at worst.
There is still another remaining alternative. Something happened to the world where it 'fell' from the intended perfection set out by God. In this scenario, God gave the universe property X, and the property of X is such that the universe was susceptible to becoming an imperfect universe. Had God not given the universe property X, then the universe would be 'perfect' but not with the property X feature.
How is this possible? If God gives X, imperfection is possible or certain. If God doesn't provide X, perfection is certain. So, why would a perfect God provide X at the cost of imperfection? Does this imply a creating mistake and a God who does not conform to the standard of perfection?
Not necessarily. What if a situation develops where 1) property X is required for perfection, and 2) property X leads to imperfection, and 3) without a universe the world is not perfect? This is Catch-22, a Creator's worst nightmare? The Creator is forced to make an imperfect decision by his own standard of perfection.
There's a few problems with this set-up. What actually defines perfection? Is it God, or is it a set of axioms which co-exist with God that when all the theorems of this formal system are derived it leads to imperfection? If perfection is the highest standards that exist, then if some blemish or some 'imperfection' is what exists, then by definition this 'imperfection' becomes 'perfect'. In other words, its only imperfect if the situation could have been otherwise by making a decision that could have been made better. In a situation where the apparent imperfection couldn't have been otherwise, this is no longer a failing but another specific property of perfection, just in another form.
So, getting back to the 3-way hypothetical scenario, God is forced to choose the best possible scenario between 1) creating a world without property X, not being to keep the world moving in the direction of perfection, or 2) creating a world with property X leading to imperfection, or 3) not creating a world and not delivering perfection according to the standard of perfection that exists. Whatever is the best possible option also ends up being 'perfect' since no other options exist that were better according to the standard of perfection.
Well, let's look at each one. If (1), then our world lacks property X, which might have brought perfection but a whole bunch more of unpleasant consequences. If (3), then we wouldn't be here to ask these questions. If (2), then we have property X, but the imperfection we see is due to X, and as imperfect the world appears, if God would have chosen (1), the world would be much more imperfect (i.e., not meeting the standard of perfection).
All 3 choices look a little disappointing, though. Why can't God have his cookie and eat it too? Why can't the world have property X and still appear perfect throughout, and then no one would ever know otherwise. Why does the world have to fall short of the standard of perfection, and then sort of like a cop out, God gets 'off' scott free from this by admitting "sorry folks, but there weren't any other options, so it's perfect nonetheless". Although, one could equally ask, why is logic this way versus this other way. In short, we can ask many questions of the world and ask why this or why that, but the one question we cannot ask - because their is no answer to that question - is why were there no other options other than the fall from this standard of perfection leading to imperfect consequences. Sure, God is off the hook in such a scenario, but the world is on the hook so to speak. Why? The answer does not exist. It's just that way. End of story.
Which also brings up the case for salvation as mentioned in my title. The case is that even though the world falls from perfection due to property X, the standard of perfection can be made possible if the world can be saved from imperfection. God, as the reasoning goes, is not content to allow the world to shift further and further away from a model of perfection, but would rather seek to 'save' that world by doing everything within the standard of perfection to bring it back. Such efforts is a salvation process, and one requiring 'Christ' (or process Y) where the world is to be saved and brought to a state that best reflects the standards of perfection.
Of course, there's many issues to discuss and debate, but I hope I have setforth the setting on why there is a case for salvation. The Christian message, in my view, has tenable features that are still relevant today.