My trust in Science is limited to peer-reviewed scientific research, open in inquiry and falsifiable. I am closed minded in the sense that I am skeptical of all empirical claims, particularly those lacking evidence.
And i agree with you, but also consider that in "peer review" all others (serious enough) experiments should be considered (even those with results/interpretations opposed to the mainstream view) which is not always the case because of pseudoskepticism, because of corruption by governments or by scientists groups or by money, because of "lack of credentials" (the reality has no credentials but it still exists...)
I am personally skeptical of all claims that i can't verify and observe myself. Especially concerning things which are uncertain (like human body health)