What confidence can we have in the various pronouncements of "Science"? The answer of course is that "it depends". It depends on the type of science, the methods used, the stage of investigation, and the reporter and target audience.
In the modern sense, Science is a methodology for establishing the facts and mechanisms of nature to a reasonable certainty. The facts and mechanisms must be repeatable for verification by multiple researchers. Other kinds of facts and mechanisms are outside the realm of established Science although they may be the subject of current research. The more often a fact or mechanism has been verified and not contradicted, the more established it is.
For example, the fact that a certain blackbird lives in North America can be established by multiple observations by competent observers. A single sighting of a rare bird may be a fact, but has not been established. Similarly a single experiment verifying the Law of Gravity may be true, but it is not established until the Law has been repeatedly verified and not contradicted by other experiments.
An axiom of Science is that nature operates by automatic mechanisms described as Laws. Science cannot answer why the Laws behave as they do unless it can be shown that a Law is the completely sufficient consequence of lower-level Laws.
Scientific facts and mechanisms are discovered by observation and logic. We all assume that something seen over and over again is a fact whether it is a thing or a cause-and-effect. Science goes further by deliberately testing with carefully controlled experiments involving reduction and repetition. This is a logical form called Induction. Induction assumes that repeated verification in the present proves a fact or law, and that such aspects of nature do not change with time or location. This is the highest level of proof that we can achieve and hence the greatest level of certainty. All other methods are much less certain.
Finally, all Scientific facts and mechanisms have a scope of validity. They may be absolutely true but their proved scope is limited to the range of conditions where they have been tested. For example, Newton's Law of Gravity has proved effectively perfect over a wide range of situations, but fails at the huge gravities of black holes and at the subatomic level.
Scientifically established facts and mechanisms can be used to support rational arguments about subjects outside of Science, but the subjects so supported are rational not Scientific. An older meaning of "science" just meant rational. Such logical results are much less reliable than those proved by Induction.
The "hard" sciences are chemistry, physics, and parts of biology, astronomy, geology, etc. They deal with the facts of the present, which when repeatedly verified are presumed true (Induction). Other "sciences" that deal primarily with the past or which have limited experimental opportunities are much weaker or "soft". Such are archeology, psychology, cosmology, evolution, medicine, etc. A newer problem is the complex computer models such as used in climatology.
The established facts and mechanisms of a hard science are the highest form of what we can know. Most of the core knowledge of chemistry and physics has not only been verified frequently by independent study, but are the basis of daily industrial processes which effectively repeat the tests tens of thousands of time per day. And the transistors in my computer verify our understanding of solid-state physics billions of times a second! This is as good as it gets.
Sciences that attempt to explain causes in the past have severe limitations that make their pronouncements "soft" in truth value. Such sciences cannot prove past events to the level of established, inductive certainty. These sciences may give us good reasons to believe we know causes and origins in the past but there are problems. Such science is like history, a story woven to explain facts of the past.
A proposed mechanism in the past leading to facts in the present can be disproved but not proved. We cannot observe a past fact or event, nor can we repeat a past event under controlled conditions, so inductive proof is impossible. Evidence can suggest a cause but does not prove it. Disproof is the only option. If a proposed mechanism violates established Science or evidence existing in the present, then it is presumed to be disproved. But several such proposals may meet all tests as presently known. Also such proposals are necessarily generalized and gloss over details that might prove critical, because reduction and controlled experiment to narrow the possibilities is difficult. As long as there is more than one plausible explanation, there is no way to know which was actually true. Also, another explanation may appear that was previously unsuspected, so even an established theory is suspect, and questions about the past are often never settled.
Fortunately, as for historical studies, these explorations of the past are primarily to satisfy our curiosity. They do not enhance or detract from our ability to live in the present, so the lesser truth value is not critical. Most of the popular reports of progress in these fields are just story telling. Story telling by an experienced practitioner, to be sure, but just stories nonetheless.
Some sciences have limited experimental opportunities such as psychology, sociology, and medicine. These claim truth about humans but are understandably limited by what kinds of experiments they can perform. Repeatability is a problem because identical human research subjects cannot be created and tested over and over to ascertain relevant factors and prove mechanisms. This is particularly important because humans are immensely complex through their DNA and environmental development, so there are large numbers of factors that might be important.
These sciences rely heavily on statistical analysis of measurements on subjects. Those persons are a tiny subset of all persons, so the test subjects have to be carefully selected to represent a general population, and the selection will always be in doubt. Also only a limited set of measurements can be made, so an important factor can be overlooked or misrepresented by indirect correlation with a measured factor. Many such studies rely on self-reporting which can easily be influenced inadvertently by the experimenter. Consequently any results, no matter how carefully done, may seriously misrepresent the actual case. Except in rare cases where something can be verified using hard science methods, results in these fields are always suspect.
With the recent advances in computer processing speed and storage capacity, computer modeling has taken a more prominent role in support of scientific theories. Computer models use computation and decision making capabilities to calculate the state and progress of a natural system such as the weather, fluid flow, chemical reactions, etc. When such models are based on exactly known physical laws such as in chemistry, physics, engineering, etc., the results can be very reliable, if the possibility of calculational instability (Number and Chaos theory) is carefully checked. However, in complex systems where the complete laws and data are not known nor exactly known, the results prove nothing.
In complex systems where the laws are not completely known, it has become believed that a computer model can prove understanding of a natural system and become the testing ground for theories. The method is superficially like the hard sciences. Parameters are adjusted and the model run to see if the results are the same as measurements of the real world. As if using induction, the model is presumed correct if the results match the expectations. The problem is that such modeling is not induction, based on reduction and repeatability. The measurements used to confirm the model are not the result of deliberate variation and measurement of the consequences. Also the real-world data used to start the calculations is simply not complete enough to give accurate results.
These models can be made to match past events in much the same way as a polynomial can be made to match any continuous function, but the result proves no actual understanding of the physical system or ability to predict future results. Such modeling for weather, climate, and economics has failed to successfully predict results more than a little outside the original data set. So results based on computer models need a large dose of skepticism.
Current, reported results are from investigations currently in progress, not from a long history of established results. Reports from current investigations are exciting both to the reader and researcher, but remember that Science is a long and painstaking process, and any result must be reviewed, critiqued, and repeated by others, and not be contradicted. It may be decades before the result is established or disproved.
A particular type of investigation often used in public discussions are targeted investigations and overviews, such as an environmental impact report. These reports are not science. They are not peer reviewed, not subject to long-term verification, etc. And quite frankly not done by the best practitioners. Often they overlook relevant factors, fudge results, and in too many cases are just plain faked. The closer such reports are to the hard sciences, such as architecture and engineering, the more reliable they are. The more they involve general biological or social information where incomplete or experimentally deficit knowledge is used, their reliability plummets. So extra caution is advised with this kind of investigation.
Much of what a lay audience hears about Science and current research is reported by "journalists". Quite often they are simply not knowledgeable enough to report the details or the deeper understanding of the subject. And the relevance of the imputed knowledge to our whole knowledge is mostly missed, as it often is by narrow experts as well.
What is reported in the general press and science documentaries seems to be targeted at the about eighth-grade level. This is the wow and wonder age, not yet the age of comprehensive understanding. It is hard to get any reporting beyond the introductory level.
A better but still imperfect are textbooks, survey monographs, and university lectures. Older textbooks and reporters educated using them often repeat earlier theories that have been proven false or even faked.
Most dangerously, sources usually do not discuss contradictory facts, nor do they convey the limitations of their report. The report language of new research or "soft" sciences, should be cautious and subjunctive, not definitive. Of course any topic that is entangled with political activism or correctness is very likely to be spun or redacted and hence seriously unbalanced, and reports are biased to the positive when funding is competitive.
So when considering "Science" information keep in mind the type, methods, stage, and reporter. Always ask how do they know that (type, method)? Has it been established (stage)? And who says so (reporter)?