Like you say, a lot of people don't understand much science. Its not because your average Joe doesn't have a PhD in Physics (although it would be epic if they did), but I think more because a lot of people look at scientific research as unneeded spending without understanding the benefits of science.
For example the LHC cost a massive amount of money but imo is a good investment for science, whereas some people that I know just see the figure and think
ugh what a waste whats the point of it anyway?, despite my best efforts to persuade them otherwise.
I think that the fact that science tends to be viewed as a "boring" subject at school (alongside other maths based stuff) and so tends to have people paying little attention in. I remember being at school and looking forward to Chemistry practicals, but other than that shunned science (sadly) until we did stuff about space, which sparked my interest in physics. The syllabus for science - physics especially - doesn't really seem to lend itself to being an interesting subject as there is a solid amount of maths in there iirc, which can cause less mathematically able people to just give up on trying.
As for the trust aspect, I also see this, but to be honest can't really think of a way to increase trust in science again, unless the authority back it more strongly. Although having said that the way people currently view MPs and the like, the general public might think the money should be better spent on say "defence" or MPs garden ornaments (the public were happy with that whole thing yes?
).
