Is the quality of evidence discussed in science? The credibility of the scientists? Is care taken to ensure that the evidence actually follows the theory, and not just the idea of the theory? I specifically mean with respect to Newton's "Laws", the "Law" of conservation of energy, Relativity, and Quantum Mechanics.

Rather open-ended, but the answer is "yes". For specific experiments or modern theory development, much of this happens in the process of peer review.

That's the best thing about science, to be honest - it's self correcting. If you somehow manage to publish a paper that's full of bunk, someone, at some point, will try and recreate it and point out the flaws in your work. It may take a while (like the whole sun orbits the Earth thing), but eventually science fixes its mistakes.