At least we can dismiss her latest fluff in the first sentence:
Is physical science - as some people say - omnicompetent? Can it (that is) answer all possible questions?
"As some people say" is one of the more perniciously lazy phrases in the English language. And setting up a straw man as the starting premise of an article is not encouraging. The answer to both is no. We don't know all possible questions, and science is just a tool. A very successful tool, but one with no alternative in sight (and Midgley certainly offers none).
To be fair, Midgley goes on to chatter about some very unfortunate hyperbole from Nicholas Humphrey, who seems to think we're close to solving all of science's questions, which is also an extraordinarily silly statement to make. But I can safely say that her questions are still ridiculous.