Observation is perception that pays attention to selected phenomena that one seeks certainty about. In the empirical disciplines, observation is the ultimate touchstone. If a researcher points to publicly observable phenomena as evidence for a claim, one can then go and try whether he observes the same phenomena that the researcher observed. There is nothing more that one could demand as evidence. This is true despite the fact that observation is unreliable because human perception is unreliable. Different persons observe different things, observation is shaped by prior knowledge, there are optic and acoustic fallacies etc.
These shortcomings are aggravated by the fact that many phenomena that the researcher reports, although he truly observed them himself, are not realistically publicly observable because they are not reproducible, i.e. identically repeatable. Disciplines such as ethnography are beset with this problem. In such disciplines, training in unbiased observation is an essential exercise.
The best observers are those that entertain no hypotheses. That would lead to the requirement that the scientist should not function himself as the observer, because a good scientist always has hypotheses. However, such a requirement seems hardly feasible.
Despite such justified qualms, the notion of public observability is irreplaceable, and public observation cannot be reduced to more elementary criteria.