Update: Much of the show was indeed devoted to Galileo's dispute with the Pope. Most of the commentary came from the author of a book about some letters written by Galileo's daughter. It would have been better to have more commentary from people knowledgeable about the scientific/theological dispute.
The show ends saying that Galileo's controversial book was one of the greatest astronomy books ever written, and refers the viewer to the web site for what Galileo said about tides. On the web site, you can learn that this great book espoused a completely wrong analysis of tides as Galileo's main argument for the motion of the Earth.
The show says that Copernicus's model was simpler than Ptolemy's, and that it had two motions for the Earth. Actually, Copernicus explained the Earth in terms of three motions. And it wasn't so simple either, because it used a lot of epicycles.
The Pope is ridiculed for this statement, made while sentencing Galileo in 1633:
The proposition that the Sun is the center of the world and does not move from its place is absurd and false philosophically and formally heretical, because it is expressly contrary to Holy Scripture.
Galileo had been allowed to use this proposition as a useful hypothesis for doing calculations, but not to claim that it had been proved true or to give his own Scriptural analysis in support of it.
I don't know about the Scriptural analysis, but someone should have said that modern Physics is much closer to the Pope's view on this point than to Galileo's. The proposition that the Sun is the center of the universe and does not move from its place is indeed absurd and false. Motion is relative to a frame of reference. With respect to a reasonable frame for the Earth, the Sun orbits the Earth. With respect to a reasonable frame for our galaxy, the Sun is on an orbit in the Milky Way, and rotates.
Galileo had some brilliant arguments in favor of the Copernican model, but there were some legitimate scientific reasons for preferring the Ptolemaic model. It was actually Kepler's improvements to Copernicus that gave a more accurate model. (Kepler was a contemporary of Galileo, but Galileo did not espouse Kepler's model.)
The PBS transcript is now online.
The PBS film is not as bad as some other sources. Eg, Here is a Stanford history course on Galileo that says in its course description:
In 1633 the Italian mathematician Galileo was tried and condemned for advocating that the sun, not the earth, was the center of the cosmos. The Catholic Church did not formally admit that Galileo was right until 1992.
You could not find a scientist anywhere who thinks that the Sun is at the center of the cosmos. That idea has been dead for 100 years. There is no way the Catholic Church would admit in 1992 that the Sun is at the center of the cosmos. That would be much sillier than what it said hundreds of years ago about Copernicus.