I am quite fascinated by the role of the scientific observer, the experimenter, who believes himself to act objectively.

This is a good critique. The universe appears to change when we look at it. We haven't found a way to control for the presence of the observer. In Psychology, we know that the experimenter can influence a participant. For example, a male testing a female will act different when he tests another male and vice versa. This can influence the outcome of an experiment. It is not that different from some principles found in physics like Heisenberg's uncertainty and Schrodinger's feline shenanigans.

Now what is the best way to resolve this situation? Personally, I think that we should keep more track of the experimenter's movements, behaviors, and words during an experiment. These metrics can be easily recorded with cameras and motion capture systems. Then the experimenter should analyze these data in relation to variables measured in the course of the experiment and determine whether his or her behavior altered the measured parameters. The results should be reported in the final paper. This is a lot of work and beyond the scope and resources of most studies but something to strive for.