The "ears" answer is not very helpful. Even the most experienced mastering engineers use metering as a tool to accomplish their task.
Completely, 100% disagree. We might use metering for setting levels, and I'll frequently run noise or sine tones through my analogue chain for level matching or other calibration purposes, but when it comes to the actual mastering, I am closing my eyes, listening to the music, and tweaking those knobs until it sounds better. That's it.
I feel the reliance upon the "visual" in what we "hear" to be one of the main causes of detrimental music processing in the last few years. I even sometimes get prospective clients sending me .jpg's of their waveforms in Logic, asking me if it "looks" OK! I mean, how am I supposed to reply to that? I usually come off pretty snarky by telling them that it tells me nothing, and that I need to actually LISTEN to it...
Spectral analysis can be rather useful in the low end when working in a less than optimal room in my experience, as it's pretty easy for problems in a null (or peak for that matter) to slip by you if you can't hear them. But otherwise you should always rely on your ear first.
Would you use a different analyzer for mastering than one for let's say comparing bass guitar to a bass drum?
There are different analyser settings. Generally you can vary between speed, resolution and smoothing.
Usually a setting of intense smoothing and very low speed is called mastering setting, but imho that doesn't really mean much. If you have one analyser where you can change the settings yourself (e.g. Voxengo span) you only really need 1 analyser.*
E.g. 1 drumloop here (obviously speed can not be seen on a picture...):
All with a linear slope, rather than a flat one....
normal resolution, quick speed
good for a general idea
high resolution and low speed
good for exposing detail (took the screenshot a bit too late so the kick is missing)
High resolution with smoothing, low speed (often called mastering analyser)
I find that one quite helpful sometimes, if you need to eq 2 sounds so they don't conflict, because you can see where most of the frequency spectrum is occupied.
I wouldn't pay a mastering engineer so he can look at a fancy spectrum analyser though, I pay him so he can use his experienced ears and get the mix ready for distribution.