one could claim that science is by nature self-correcting
That is rather the point, isn't it? Take gravity, for example. From Galileo's models of uniform acceleration, to Newton's Universal Gravitation, to Einstein's Relativity theories, etc. each of these guys knew that their models for gravity were incomplete. Yet, each of them served as increasingly accurate tools to observe the universe and make predictions about its behavior. Someday, somebody will figure out how to make a model that ties gravity out between quantum and classical mechanics, which will be more accurate still, but almost certainly will not be absolutely complete.
When you say "science" do you mean the Scientific Method? The scientific method remains one of the most reliable methods for verifying truth. Intelligent design, astrology and alchemy may have adherents that consider them "science" but that doesn't mean they are. Science is the Scientific Method. Period. Full Stop.
You brought up the example of cholesterol. Based upon the science of the time, an increase of LDL cholesterol corresponded with an increased risk of heart problems. That is still true. They simply said "eat less of this bad stuff" which seems intuitive. If science research mirrored religion, that would be the end of it, and maybe the rest of western civilization would have followed the Jewish and Islamic faiths into the abyss of bacon deprivation. Thankfully, that is not the end of the story, scientific work continued (yes, that science) and now we know that dietary consumption of cholesterol is not the primary contributor to LDL levels. Will there be another study that shows that eating certain foods, perhaps in combination, do, in fact, contribute to high LDL levels? It wouldn't surprise or distress me if there was. I would not want to wait until there could be absolute certainty that eating mayonnaise in combination with french fries somehow appeared to skyrocket LDL levels. I would like to know soon enough that I can do something about it, even if that information gets refined later on.
You could make an argument that there is a "scientific community" that is increasingly accommodating shoddy science. But that isn't a failure of science, any more than a nut job driving a car bomb screaming "Allahu Akbar" is a failure of religion.