It appears that in any effort to qualify data that has been experimentally collected as evidence in order to support or refute a scientific theory, there is the possibility that the qualification could be erroneous.
Yes. A modern understanding of evidentialism doesn't deviate from a fallibilistic interpretation of epistemological truths. In fact, the take away from the post-positivist effort to completely objectify observation is that empirical data, a form of observation is theory laden. From WP:
Semantic theory-ladenness refers to the impact of theoretical assumptions on the meaning of observational terms while perceptual theory-ladenness refers to their impact on the perceptual experience itself. Theory-ladenness is also relevant for measurement outcomes: the data thus acquired may be said to be theory-laden since it is meaningless by itself unless interpreted as the outcome of the measurement processes involved.
Therefore, theory-ladenness goes beyond the mere potential of the introduction of error; fundamentally, all qualification and quantification is inherently normative and must be understood in the great context of the theories it is employed in, which brings us to the Duhem-Quine thesis. From WP:
In philosophy of science, the Duhem–Quine thesis, also called the Duhem–Quine problem, posits that it is impossible to experimentally test a scientific hypothesis in isolation, because an empirical test of the hypothesis requires one or more background assumptions (also called auxiliary assumptions or auxiliary hypotheses): the thesis says that unambiguous scientific falsifications are impossible.
It seems that there is never support for arguing one theory to be plausible in comparison to any other theory because of the inability to provide definitive evidential support for a theory.
This of course is the underdetermination thesis. From WP:
[U]nderdetermination or the underdetermination of theory by data (sometimes abbreviated UTD) is the idea that evidence available to us at a given time may be insufficient to determine what beliefs we should hold in response to it. The underdetermination thesis says that all evidence necessarily underdetermines any scientific theory.
So, what seems to be the modern stance in philosophy of science is the idea that human beings fallibly introduce normativity into observations, both linguistic and through measurement, by choosing what and how to describe and measure. When done well, peer review helps to minimize and shape the nature of errors and choices, but even when done highly competently, the theoretical paradigm in which a science conducts its business helps to determine the results of the research by providing a bundle of hypotheses and theories in which the work must be evaluated. Of course, Popper famously argued that neither verification nor confirmation settles the matter with demonstrative logic (deductively valid), but rather in a coherentist spirit, scientific research is falsified. From WP:
Popper contrasted falsifiability to the intuitively similar concept of verifiability that was then current in logical positivism. His argument goes that the only way to verify a claim such as "All swans are white" would be if one could theoretically observe all swans, which is not possible. Instead, falsifiability searches for the anomalous instance, such that observing a single black swan is theoretically reasonable and sufficient to logically falsify the claim. On the other hand, the Duhem–Quine thesis says that definitive experimental falsifications are impossible and that no scientific hypothesis is by itself capable of making predictions, because an empirical test of the hypothesis requires one or more background assumptions.
So the sciences suffer from a tension between the probabilistic and inductive methods of math and logic which attempts to confirm, and the certain and deductive methods of math and logic which attempts to disconfirm. And all of this happens in a broader linguistic and social framework as later Kuhn argues reasonably in his Structures of Scientific Revolutions where primacy is necessarily afforded to defeasible (SEP) and parsimonious inference to best explanation.