I think this story actually critiques many different things, not just science. Of course these critiques are all based around the way in which nobody is shown to be able to interpret the sudden appearance of the old man with enormous wings, yet everybody feels the need to come up with some kind of answer to his mysterious presence amongst the villagers. Science, together with religion, is critiqued in this way through the character of Father Gonzago, who, having established that the old man is definitely not an angel because he does not speak Latin, sends letters to Rome to try and receive guidance on what actually he is. Note the following quote that describes the kind of advice he receives:

Father Gonzaga held back the crowd's frivolity with formulas of maidservant inspiration while awaiting the arrival of a final judgment on the nature of the captive. But the mail from Rome showed no sense of urgency. They spent their time finding out in the prisoner had a navel, if his dialect had any connection with Aramaic, how many times he could fit on the head of a pin, or whether he wasn't just a Norwegian with wings. Those meager letters might have come and gone until the end of time if a providential event had not put and end to the priest's tribulations.

The best scientific minds show themselves to be absolutely baffled by the old man, and focus on redundant and irrelevant questions that do not head towards any conclusion or solving of the problem that the old man represents. The way in which these letters displayed no "urgency" and even focused on ludicrous assumptions such as "how many times he could fit on the head of a pin" demonstrates the way in which science and the scientific method is being critiqued in this story.