A few interesting and fun facts about the augmented scale:
The tune "Hoedown" on Oliver Nelson's The Blues and the Abstract Truth uses the ultimate cliché augmented scale lick that many people know. Oliver Nelson also uses that very lick in a couple of solos on the record.
As far as practical applications, the augmented scale is interesting because it is never completely "right" over any commonly-used jazz harmonies. On the other hand, it can almost fit over just about anything, give or take a "wrong" note or two. For example, since the maj 7#5 could be used as an upper structure for most, if not all, of the chords diatonic to the jazz melodic minor scale, an F augmented scale could be played over:
(D melodic minor)
Fmaj7#5/D (which implies the sound of D min/maj7)
Fmaj7#5/E (which implies the sound of E Phrygian natural 6th)
Fmaj7#5/F (which actually is Fmaj7#5)
Fmaj7#5/G (which implies the sound of G Lydian dom or G7#11)
Fmaj7#5/A (which implies the sound of A Mixolydian b6)
Fmaj7#5/B (which implies the sound of B half diminished natural 9)
Fmaj7#5/C# (which implies the sound of C# altered which is dom 7 w/b9,#9, #11, b13 )
The augmented scale can be used to good effect on one chord vamps, as well. I've noticed Michael Brecker seemed to do this often. He'd sometimes play fast arpeggios of the major and minor triads in some symmetrical pattern, for instance.
"Giant Steps" and the bridge to "Have You Met Miss Jones?" consist solely of major key centers that are major thirds apart. Remember that the augmented scale contains three major triads major thirds apart...or, the cheater's way of playing "Giant Steps."
One other note: interesting harmonies can be derived by creating polychords from the three major and three minor triads (or even by combining the notes in the scale randomly).
Here's an example from the C augmented scale (could also be called the E or Ab augmented scales):
Play an E minor triad on the top three open strings. Below that, play an Ab triad on the other three strings. Play Ab on the 6th string 4th fret, C on the 5th string 3rd fret, and Eb on the 4th string 1st fret. Also, try inverting the Ab triad up the neck, staying on the bottom three strings so that the E minor triad continues to be playable on the top three strings. Particularly cool is the Ab triad an octave above the original one, as you get all half steps between the notes on the bottom and top three strings.
As usual, I accept no responsibility for the consequences of trying any of this stuff at someone's wedding. Then again, I've occasionally been amazed at what I can get away with on solo guitar gigs when no one's listening. No riots as of yet.