"Science is a process, a way to find truth. It is not in itself truth."
We mostly all know this.
The issue is populism and communications.
When we use 'Science' as a basis of infallible credibility in some areas, then it's understandable that some are 'shocked' when that infallibility is obviously not true, and then people become jaded and lose confidence.
There's no language to differentiate between the murky greyness of some things (i.e. memory and recall), and the relatively unambiguous results of other bits of research (i.e. acetaminophen is safe).
Why should the non-scientific public, even sometimes, have confidence in a system that is so often very wrong? How are they supposed to know which bits are 'effectively true' and which are 'grey'?
From the outside, it looks like Science is being simultaneously authoritative (to the point of moralizing) and in other areas totally wrong but lacking in self awareness while saying 'Oh, that was wrong, bu Science is a process of discovery, it's not always right' etc..
Given that Science is constantly 'changing it's mind' it's perfectly reasonable for regular people to doubt Climate Change science: the 'authorities are often wrong, ergo, they may very well be wrong here'.
If Science doesn't have a way of effectively (and by that I mean simply and clearly) communicating the degree of confidence in something, then we're playing a very dangerous game with credibility of the institution.