Let’s now address 2, the implication that because scientific theories change they are unreliable. This is usually contrasted with religious doctrine, which remains unchanging. We generally perceive someone who constantly changes his mind as fickle and unreliable, while the person who can always be trusted to be true to his word and not change his mind is steady and virtuous. But claims about how the world functions are not people, and this is not a question of loyalty. This is instead like the person who insists that the sky is purple because that’s what his parents told him, and when you take him outside to show him the sky is blue squeezes his eyes tightly shut.
Scientific theories are our current best guess as to how the world functions, and so are subject to change as we uncover new evidence. Religion, on the other hand, as the revealed wisdom of the Creator cannot change. For religious doctrine to change implies that God was wrong. At the very least, it implies that generations of pious, learned paragons of faith misinterpreted God’s message. This rigid adherence to tradition is not a strength. While we all crave certainty, an unwillingness to change which produces the illusion of certainty is not the same as actually having certain knowledge of how the world functions. The reluctance of religion to change in the face of scientific discovery has led to some strange confrontations. The most famous is Galileo’s run-in with the Catholic Church, and while this was mostly his own fault (he insulted the pope and was notoriously rude towards those who disagreed with him) it, and the even more severe treatment of some of his predecessors, stands as an example of the difficulty of changing doctrine and the lengths of suppression organized religion will go to in order to avoid doing so.
Judaism itself has been left with many, many examples of counter-scientific articles of faith, ranging from the age of the Earth to the creation of the Earth before the Sun. While many of these sorts of difficulties can be gotten around by using non-literal interpretations, if we take the great rabbonim of past generations to be infallible (as much of chareidi Judaism does) we’re forced to accept things like spontaneous generation and Aristotelian physics (particularly the four elements).
What's worse, religion's claim to be unchanging isn’t even true. Religion has changed, often radically, and often in response to social and scientific advances. At a certain point, the evidence is overwhelming, and religious texts are reinterpreted allegorically to fit with the newly-acknowledged truth. There are few people today who claim that the Earth is flat and has corners or that the Sun goes around the Earth. Those who do hold such views are rightly seen as the lunatic fringe.
The real difference between science and religion is that for a scientist, acknowledging mistakes is okay and, “I don’t know,” is an acceptable answer. For the religious apologist, changes to the religion have to be ret-conned so that they were part of the tradition all along, and, “God did it,” serves as a handy answer to any mystery. For the scientist, mistakes are opportunities for improvement and mysteries are exciting new areas of discovery. For the apologist, mistakes are at best a demonstration of the puniness of humans attempting to understand God’s will and mysteries are an opportunity to marvel at His greatness.