"But now all sorts of well-established, multiply confirmed findings have started to look increasingly uncertain."
Good! That's what science is all about. Making theories that can later be "disproved" or "confirmed". It's when you cannot disprove something that it is no longer science.
This means nothing can ever be confirmed though -- you never know if you'll learn something later to disprove what you think you know now. Which in turn means a certain level of humility is required. To me, that's where science falls short -- anything that doesn't fit what is currently 'known' and 'proven' is not taken seriously.
Good! That's what science is all about. Making theories that can later be "disproved" or "confirmed". It's when you cannot disprove something that it is no longer science.