Of course, the microscope was an analogy -- e.g. in a microbiology seminar, students look privately into their own microscope, each observing different preparation of the same strain of bacteria, but (not surprisingly) the results match.

Obviously, when we talk about self-knowledge, no one can look into your mind. But -- and it's a big BUT -- in terms of self-knowledge, you observe what observer is not. And since it's an observation "in negative", the problem of subjectivity (which you say disqualifies such observation because of its private mode) does not apply.