I'vew heard the Marcel Moyse "falling excersize" is a pretty common, well-known flute warm-up among real flautists, not sax-playin' fakers like me. What is this "falling excersize"?

Hi I believe that youa re referring to one small part of the De la Sonorite book by Marcel Moyse.
This is an exercise for developing tone quality.

It is played with a chromatic scale.
1: Quarter note B2 (Above the staff.)
Descend 1/2 step to a Bb/A# dotted half note.
Repeat.
2: Quarter note Bb2 (Above the staff.)
Descend 1/2 step to an A dotted half note.
Repeat.
3: Quarter note A2 (Above the staff.)
Descend 1/2 step to an Ab/G# dotted half note.
Repeat.

Descend in this manner down the chromatic scale to the lowest notes.

Then go up from B2 to the highest notes in similar manner.

This again, is only part of the book and also only part of a larger exercise. It must be listened to so that the best tone, control and tuning are used for all notes.