Some ancient writings are accurate, some are not.
It would have been good to see an example or two to support this and how one arrives at the conclusion that some are accurate and some are not.
Quite right, but there are so many to choose from!
Looking at the ancient Greeks, for example, Archimedes did good work on density and other things and Eratosthenes made a remarkably good estimate of the diameter of the earth. Both used an approach that we would recognize as scientific, with experiments.
Aristotle tried to do physics without experimenting, got things wrong much of the time, and probably delayed the appearance of modern science by hundreds of years. The history of the writings of Aristotle is a good example of the harm that can be done by slavish adherence to ancient texts.
Other examples are the medieval herbals. They mixed sound (probably folk) knowledge with outrageous balderdash.
If writings are supported by modern knowledge, we can regard them as accurate. If they are refuted by modern knowledge, we can say they are inaccurate. Otherwise, we don't know either way. We can get an estimate by considering whether the material is consistant with the way we now know the universe works. Personally, I think that the "wisdom of the ancients" notion is chiefly useful for making sensationalistic TV programs.
In these comments, I am just referring to what the texts say. They can be good evidence about the times in which they were written whether what they say is accurate or not.