[The following comments are those of an INTERMEDIATE LEVEL PIANO STUDENT, mostly self-taught at this point in life, no teacher possible right now I'm afraid. I am highly educated, erudite, witty, urbane, and generally a human wonder, but I have no qualifications in music.]
brogers70:
I suspect that any individual Hanon exercise, and for that matter a great many other exercises, can be used to help improve several aspects of technique AT THE SAME TIME.
Consider Hanon no. 1: Play it in Eb major and E major (with the same fingering as for C major of course.) Offers a few interesting challenges, does it not? For example, descending RH fingers 4 and 5? Getting fat stupid fingers cleanly between the black keys? Staying relaxed?
Playing major 3rd intervals with fingers 4 and 5 is a real problem for me, so I like the Hanon exercises that force me to do it all up and down the keyboard in different keys in the space of a minute or two. Not to mention the attention that must be paid to keeping finger 3 from causing trouble between the black keys.
You can work on a half-dozen different aspects of technique in the space of a few minutes with any Hanon exercise, by changing it a little as needed. For example, try holding down all the keys as you play, only releasing a key when that finger has to move. Or hold down just one key while the others play detached, or two keys, etc. like in Schmitt. Or stretch outside the given range. It never ends.
The great thing about Hanon and Schmitt -- at least from an intermediate-student point of view -- is that the exercises are so simple! You learn each exercise in 10 seconds and then spend another 90 seconds playing all kinds of variations on it, in random keys. In 10 minutes you can really cover a lot of ground.
If you have a 25-key MIDI keyboard, you can even practice a bit, with one hand at least, while taking a long hot bath.
You also have the choice, when the hardasses aren't looking, of doing your Hanon mindlessly like pushups, while you read the news or daydream about the girl next door. Then when the erection gets embarassing, you can get all pianostreetforum and focus on rotation, relaxation, feelings of personal inadequacy, and so on.