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The source tracks are everything! This is why I'm huge on getting the best possible raw sound. Simply put, the better the initial recording sounds, the better the finished product will sound.
A great master can be both dynamic and powerful. You should hear every subtle detail, yet not be bombarded by them. It should feel good to listen both, loud and soft, and also adhere to industry LUFS (Loudness Units Relative to Full Scale) standards.
Mixing is essential to get a professional sound. A good mix will give you a sense of being in an environment. If done well, you should get lost in the song, and forget about "the mix" entirely.
A good production helps the song and can give the artist "their sound". A producer should have a refined opinion and is able to use their experience to accentuate the song's ability to invoke emotion. A good producer will take on full responsibility for the outcome of the product.