Not really, there were actual problems with the Copernican system, mostly because it still required epicyclics. The favored system at the time was the Tychonic system, and what actually allowed heliocentrism to prevail was Kepler's introduction of elliptical orbits.

Some of Galileo's points, for example his explanation of tides in term of heliocentrism, were downright wrong---which is fine, but trying to mix theology and astronomy, which he did, and putting the pope's theory in the mouth of a character called "Simple" were not the best political moves.