The development of such physical theories as Galileo's is no straightforward process, and often takes the wrong directions, and unnecessary pit stops, and the discarding of less accurate theories in exchange for more robust ones: physics is not just a collection of facts and principles, it is the process by which general principles that describe natural phenomena are generated.
Also, no such theory is treated as the final truth, as there is always a possibility that new observations will require the revision of theory, or replacement entirely: we can disprove a theory with contradictory observations, but we can never prove that a theory will account for every possible observation.
Consider Galileo's theory with a bit more specification, such as dropping a feather and a cannonball, which certainly do not fall at the same rates.
This is not an indication that Galileo's discoveries were incorrect, but rather that the theory he used to explain them were incomplete: His theory is correct in a vacuum, which eliminates the effects of air resistance on falling objects.
What this means is that Galileo's theory has a range of validity: it applies only to objects for which the force of air resistance is less than the weight.