"If science is so perfect then why have there been so many mistakes and false assumptions made in science in the past? And if there were mistakes before, why wouldn't there continue to be mistakes being made now?"

It's simple. The vast majority of people (including scientists) are stubborn, stupid, and easily buffaloed. The mistakes made in the past come not from the scientific method itself, but people using the scientific method improperly.

The important thing about science is that all good hypotheses/theories are testable and falsifiable. The same cannot be said of some proponents of alternative medicines, who argue that the methods they employ cannot be proven to work because such methods are beyond falsifying and testing.