One line of reasoning that JW's and other fundie Christian religions use is that "Christian Morals" are being discarded.(It is my view that "christian morals" is code for "control tactics") Sexuality is more out in the open. Women are making great strides in gaining equal rights.(they don't even need a "head" over them... shock!) So I think this is what they mean when the "world is getting worse". It means worse for them, not for the real world.
The real world has problems and always has. But as Void Eater has pointed out, there have been great gains in many areas of life. Human rights and slavery, while not out of the woods, is not as big a problem as it once was.
Utopia/paradise doesn't exist, and it never has. All of us have to make the best of the situation we find ourselves in. We need to do what we can, be a responsible citizen, but also realize we are limited in what we can do. Being realistic is a challenge. There are so many things out of our control with the world, and some out of panic turn to religion and their utopian fictionalized view of the future for comfort. They get scared because they see bad things in the world and cant' control them. Other's assess their situation, do what they can, and go to bed with a good conscience.
On balance, the world isn't getting worse. Imo.