Just a couple of comments to add to the already good stuff above:
(sorry, fairly long as some of this comes from my course section on mixing)
#1 Why do we mix - there is only one reason why ...
We mix to master. The entire point of mixing is to complete that stage of the process and move a great mix to the mastering stage. Knowledge of that defines and establishes the goals to set in the mixing stage.
#2 Establish targets to hit. While much of the discussion focused on analyzers (which is the OP's title - but in the context of mixing), it is necessary to establish targets to hit in the mixing stage. As discussed above tonal balance is a big one - I would only add that a frequency analyzer should be confirming what you hear, not influencing what you hear. In other words - spending some time and money on your monitoring environment is far more valuable in mixing than any plug you'll ever buy. I also prefer to preview a great sounding CD in my monitoring environment before I begin mixing. We all have some great CD's and I use them to reference my room (I also follow Bob Katz's monitor positioning methods as well as RTA in the room to match the analysis in the box prior to mixing) All of that effort ensures that what I am hearing is being confirmed by both analyzers (one in the box and the other in the room) Obviously this tells me what's happening in the room and prevents me from making changes that don't translate to other environments in the mix. I'd also add that once you have your room down, listen to good CD's in there for a day or two. Inform your ears about what the room sounds like. Humans are pretty smart and pretty dumb both at the same time. Educating our ears to what a monitoring environment sounds like is what makes analytical tools useful. I would only add on the spectrum side of the mixing target that I don't think in terms of frequencies when I mix unless I am solving problems - My initial approach to mixing is to work in octaves. In other words I consider the 11 octaves and how they are being covered in the mix. I use Sound Forge's statistical analysis with three presets for full bandwidth, HPF and LPF settings. I compare those statistics to other material with a good tonal balance and make my mix, EQ and compression changes accordingly.
There obviously are other targets in the mix stage - my comments here intend to focus on the spectrum side...
livin' the life in Sonar 8.5.3
Best
-D