Pashuteh Yid:
You asked for an example where Chazal’s knowledge was ahead of the scientific knowledge of the time. How about the length of a lunar month? Unfortunately, almost all my possessions are in storage right now, so I can’t look up the exact figures, but if you look at the amount of time Chazal say it takes for the moon to renew itself, it is 29.????? days. If you look at the historical data from scientists, you will see that as their tools and knowledge progressed, they have come closer and closer to Chazal’s number.