Instead of looking at minuscule symbols that relate to either things or people, let us look at the major symbols that make up the meat of this play: Galileo's findings and the Roman Catholic Church. Both of these large concepts/institutions are the main crux of this work of literature and prove the main conflict: science vs. faith.
In short, Galileo's findings symbolize science. Galileo finds that the earth revolves around the sun. He has enough observations to prove this as fact. The play is about the conundrum that results. Science, of course, is proven by observation. Galileo uses his telescope to confirm his findings (and ends up losing his eyesight as a result). The unfortunate thing is that his findings contradict important teachings at the time.
On the other hand, the Roman Catholic Church symbolizes faith. The Roman Catholic Church had long taught that the sun revolved around the earth, showing that God has the earth, the main part of His creation, as the center of His focus: humanity. At the time of Galileo's findings, the Church was not about to change its position and simply persecuted those who taught or believed differently; therefore, the Church continued to impose its rules. The entire point of faith is that it cannot be seen or proven. Faith has to do with simple belief. The idea that the faith (here represented by the Church) could be "wrong," might call people's belief into question.
Investigation of these symbols, then, show the conflict of this play as one of science vs. faith (Galileo vs. the Church). The irony is that, in the time since, the Roman Catholic Church has long submitted to Galileo's findings and admitted them as truth within the mystery of God's creation.