When thinking about integrity in science, it can be helpful to think of the various phases through which a particular scientific field usually passes. This is rather oversimplified but nevertheless a helpful visualization.
Three phases can be considered:
Frontier. This is the early stage of a particular question or issue. This phase is usually characterized by no data, no theory, or both. Research is focused on developing the theories or devising experiments to obtain definitive data.
Controversy. In this phase, there are contradictory theories that explain the data, or contradictory/incomplete data relating to a particular theory. Research is focused on carrying out differentiating experiments to resolve the question of which theory or model is correct.
Consensus. Finally, a phase is reached where the theory and the data are accepted by the active researchers in the field. Research is no longer focused on determining the correct theory or obtaining definitive data, but on working out details, implications, and expanding into potentially new frontiers.
These three phases represent the degree of maturity of a scientific field. It is judged on the basis of those who are professional scientists actively working and publishing in that particular field. They are the ones most qualified to assess technical work in that field.
This is why it is possible to hear the words "there is no controversy" when clearly there is a major controversy, as is often the case when discussion global warming or evolution. The "controversy" phase is determined by the community of experts working in that field. When that community is in consensus, then there is no further controversy, even though there may be alternative scientific papers coming from outside the community, or even a few isolated ones from within the group. In the media or in groups outside the experts, there can still be tremendous controversy.
The consensus opinion of the experts may be wrong. However, if the consensus is supported by a strong set of differentiating data, then the opinion is not likely to change in the future. I cannot think of any example in this stage that has changed. Virtually all examples where "science was wrong" are cases where the work was in a frontier or controversy stage.
Who is best qualified to judge the stage of a particular area of study? Those actively working in that field. Don't hesitate to ask them directly. If skepticism comes from outside that group, we must ensure that a response comes from the expert group itself.