Is this really a solid objection to Christian regard for ancient Scripture? No, for at least three reasons:
1) It is simply not the case that everyone prior to Columbus (or take your pick of any other figure) thought the earth was flat. Plato, in the Timaeus, considers that it is round, Aristotle in On the Heavens, considers that it is round. Aquinas, in the Summa, considers it well known that the earth is round. In fact, it’s hard to find anyone in antiquity who thought the earth was flat.
2) The Bible makes no comment on the topic
3) The logic of this objection is not very weighty: if certain ancient people had some largely unspoken assumptions that later turned out to be false (e.g. that all swans were white), why would that therefore mean that key topics they actually did speak passionately about were also false? Imagine that in 500 years, people are looking back at the year 2015, and casting everything we believe as spurious, simply because we don’t yet know that disembodied travel is a scientific possibility (obviously I made that up). Wouldn’t that make you feel a little indignant? If the point of the clichéd saying is simply that some beliefs from the past have proven to be wrong, who wouldn’t agree with that? We are in tomorrow’s past, and some of our beliefs will also turn out to be wrong. That’s the nature of human finitude. But the Christian claim is that in the midst of human finitude, God has spoken.