Being able to buffer curves and having the ability to mute/unmute tangents are useful tools when refining an animation. Using these tools along with ghosted frames and motion trails (to check spacing and arcs) will give you the tools you need to create high quality shots.
Let's say you had an animation of a bouncing ball (and who doesn't?) In this animation, you probably are using more than one animation curve so it should suffice for this example. You are able to temporarily silence curves that are interfering with your motion by selecting the channel(s) in the graph editor and muting them. This will cause the curve(s) to flatten out and behave as though there were no keys set on them.
You can find the mute item under your Curves menu of your graph editor.
Using our simple bouncing ball example, you can try muting your horizontal anim curve so you can focus on the vertical motion of the ball. Conversely, if you wanted to focus on the rolling and settling of the ball, you could then mute the vertical motion. If you were swinging a pendulum in a figure 8 motion, the same rules still apply.
When muting a curve in the graph editor, there will be a little symbol next to the channel indicating that it has been muted. The original keyed anim curve will become a dotted curve and the temporary replacement will become a flat solid line. You can unmute the curve(s) from the Curve menu in your graph editor.
Handling one dimension at a time by muting channels you temporarily don't need is useful but sometimes this isn't enough to help you tweak efficiently. At times, you need to edit two or more channels at once and when this happens, your arcs and spacing become priority.
To check out your spacing, go under your Animation menu set and under the Animate menu, you'll find the Ghost Selected item. Go ahead and reset the settings one by one based on your situation. I usually like having 2 keys ghosted after and 1 key ghosted before. Or having two steps ghost after and 2 steps ghosted before.
Once your spacing is neatly arranged, you will want to double check the arcs that your objects are moving in. Do this by switching on Motion Trails. You can also find this one under the Animation, Animate menu. You can have it update when you change a key--you can also have different display styles for the tool. My favorite display style is the line type because it visually plays "connect-the-dots" with all my keys.
As far as I know, there is no magic "remove motion trail" button. However, you can delete the trail by selecting it and pressing delete.
Using Buffer curves can be a life saver. As animators, we're used to having multiple files for the same scene and sometimes this is true even if there is a minor tweak on a curve. Buffer curves can make your work more efficient by allowing you to test out different key configurations without throwing away all the hard work you put in.
Before you use Buffer curves, you need to switch them on in the graph editor view menu.
Once you are ready to tweak an anim curve and turned on Buffer curves from the view menu (in the graph editor), you can select the curve and go to Curves->Buffer Curve Snapshot. This "saves" your current configuration for your current maya session. You can now start tweaking until you can't tweak anymore. You'll be able to see the original curve ghosted in the back but if you don't like what your new curve is doing, you can always go to Curves->Swap Buffer Curve.
A small note on weighted vs. non-weighted tangents: I disagree that it should always be one or the other. I think it's fair to say that it's best to use the right one for the job. I generally start out with non-weighted tangents but if I find my particular situation better fitted for weighted, then I will switch to weighted tangents.
A pro of weighted tangents is that they require less keys since they use different math to interpolate the curves. A pro with non-weighted tangents is that they can scale uniformly without a fuss.
A con of weighted tangents is that they do not always behave when you scale them. Sometimes the tangents reset and act funny especially if you have stretched too much. There is plenty round off error to pull this off successfully. A con of non-weighted tangents is that they require more keys to do the same thing a weighted tangent can do.
I hope this follw-up tutorial has been helpful.