Science is good stuff. Open discourse, critical thinking, unconventional approaches: all good stuff. I've spent a lot of effort over the past few years trying to promote science as the basis for how medicine is practiced and as a larger player in forming public policy (rather than merely economics--the king of all public policy).
Although I find 'intelligent design' arguments to be compelling and interesting philosophically, they are not science. There's a place for both philosophy and science in the public schools, but they should be appropriately designated (not masquerading as one another).
I suppose this division in my thinking also applies to religion and science. Mormonism, at least, operates with different assumptions than science, and so comparisons of science and religion are often erroneous from the start. For example, in science, natural laws are thought to be consistent everywhere and at all times. In religion, on the other hand, this idea is specifically denied, making miracles and other scientifically impossible phenomena (omniscience, omnipotence, separation from time and space) possible. You can't get valid conclusions when you are combining two different universes of discourse where the axioms don't match up.
Further, much of religion is presented in a metaphorical manner that is appropriate for a particular society, and making strong conclusions from the specific language of scripture leads to misunderstandings regarding the scientific veracity.
There have been times I've attempted to really understand some particular conflict between science and religion. There are professors all over the country looking at some of these issues--anthropological, physics, genetics, etc., and they bicker (sometimes in professional journals) about how it all relates to different religions. A little research turns up many resources claiming an impartial presentation of the facts on a given topic. However, the more I read the more I find rebuttals and rebuttals of rebuttals and eventually realize the impracticality of learning the issue well enough to really judge for myself. There's no easy way to tell when writers have an agenda that makes them less than candid. Conflicts of interest are seldom transparent. And the issues are often very very complicated.
'Appeal to authority' is a well known type of fallacy. You can play the experts against each other till the cows come home. So, my current plan is to not give the conflict between science and religion much credence. I don't have the time or qualifications to really weigh in on whatever issue du jour happens across my way. I also feel completely comfortable disregarding the army of pundits who get in my face and claim that "science has shown that..." or "there is undeniable evidence that...". I DO know enough about science to know that many of these people are disingenuous, or at best, idiots. So, I don't feel the need to justify myself.
Ultimately, as in the words of Bruce R. McConkie, "truth will never be in conflict with itself." We just have to be cautious and not throw out the baby with the bathwater. Both science and religion are clarified over time.
I love science. I revere science. And when science seeks to tell me something about religion, I seek to tell science to go to an unfavorable religious destination. Same goes for religion attempting to short-circuit scientific inquiry by asserting its various tenets as scientifically relevant.
There are genuinely difficult issues with stem cell research, cloning, animal research, and how morality in general plays into the scientific establishment. Here alone I feel compelled to find common ground in my own mind. And sometimes I don't find it. But luckily, as such problems relate to the whole of society, they can be appropriately codified into our laws when the need arises through public dialog and representative government.