Edit: Yes, I'm a page late, I'm trying to actually do work at work for once too.
The fundamental problem with "mixing faith and science" is that once you admit *ANY* conjecture or idea that isn't supported by other evidence, you completely completely change the character of your system in ways that frequently end up being disastrous.
As an example, I'd like to use mathematics. As everyone (hopefully) knows, no two integers are equal. If a - b = 0, then a = b. Now, suppose that you belong to a mystical religion that believes that God created mathematics and, for mystical reasons which are beyond human comprehension, set two unique extremely large numbers as equal. These two numbers are, let's say, absolutely gigantic - larger than the human brain could comprehend, larger than any computer in the world could store, and only God knows their exact value. Of course, they aren't big enough to be indescribable in some kind of mathematical notation, and that's where the house of cards starts to fall down. Once you can describe them, you can subtract one of the two from both, and end up with two different numbers that are both "zero", since you're subtracting the same number from both and zero is still unique, or was before we started this exercise. What you end up with is an entire hierarchy of "shadow numbers" that are just like normal numbers, except.. they only exist independent of regular numbers because you asserted something without proof.
Nearly the exact same argument applies to physics. It might seem innocuous to attribute just ONE little "matter from nothing" incident to God, but once you do, you destroy any basis that your theories have in reality. If you let God violate the laws you think govern the universe, you have no laws, because you can never know when something's happening because of explainable physical phenomena and when it's happening because God woke up on the wrong side of the bed and decided to not play by the "rules". It makes any attempt to enumerate the rules pointless, because at any instant, God could interfere and totally change things. The only alternative is to bind God to the laws of physics as well, but then he really doesn't deserve the title, does he?
A lot of religious people try to get around this by saying that God can, but won't do certain things, but that's nothing but an evasion - as with most faith-based assertions, it's just using faith to support other faith. Why do you believe that God won't do certain things? Because he told you, of course. Why can't he be lying? Because he's God, and God doesn't lie. Why doesn't God lie? Because God told you he doesn't lie. Repeat ad infinitum.
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