One piece of advice from the book is that a good mix starts with a good arrangement - you need the right starting elements in order to have a great product. In Jazz, some mixing engineers would actually simply record the artists playing, no compression, EQ, levelling etc - the musicians were so good that they produced a great recording without needing to mix the piece, simply because they each played in their own range, the instruments didn't clash, and they were really dynamically on point.
There are 5 main elements that are cited as being key to a good mix:
(note that an "element" can consist of more than one instrument; assuming both instruments are playing the same rhythm and/or melody, they can make up a single element)
Foundation: Bass/Drums. The rhythm section.
Pad: Long sustaining notes/chords.
Rhythm: A counter-rhythm to the Foundation. This can be as simple as double time hi-hats (think dubstep), congas, or a rhythm guitar strumming a different rhythm than the drums/bass.
Lead: Vocals, lead instruments, solos.
Fills: An answer to the lead, an instrument that "fills in" the space between lead lines.
So what I've taken out of this so far is that its good to think of your mix in this way; these 5 elements can really fill in your whole song if used correctly, and then you don't end up with tons of different elements trying to compete for space/attention; they work together.
Not only is this a great way to think about composition, its a great way to simplify your mixes!
Hope this helps someone else.