It has a gigantic gaping epistemological problem as you state it, which is that if you think the bias is strong, it reduces to being indistinguishable from postmodernist anti-objectivity; and if you think it isn't, you're left with pragmatic modernism, which in practice modernism always was anyway (at least as far back as Popper...I grant that Carnap was a bit less attentive to phenomenology), except without the intellectual justification to go beyond scientific realism (which has always struck me as just the positivist intuition catching up with the pragmatic realities of science).

Anyway, science is as good of an authority as it is, because it is constantly demonstrating and documenting exactly how good of an authority it is. That's the point! It is not just "another biased way of seeing the world". It can be hard to meet the necessary preconditions, but the entire point of the endeavor is to render the outcome as immune to the biases of the agent as is humanly possible. "We still fail at it" is in no way the same statement as, "Oh, it's just another biased way."

Indeed, this sounds more like a typical postmodern perspective than like, say, Bhaskar. (At least early Bhaskar. Late Bhaskar I'm not so sure about.)