I believe their dance simply represents Max's ascension to adulthood and constitutes a beautiful and poignant act of remembrance.
TotalFilm actually listed it as one of their top 20 film endings ever, commenting:
The Ending: His play a triumph, and an imperfect but stable compromise
reached with Ms Cross, Max Fischer looks ahead to young adulthood with
a new girl on his arm and a new perspective on his own myriad
It's been a rocky ride for the young firebrand, but the sense of
emotional achievement is palpable.
Goosebump Moment: Right as those "all the world's a stage" curtains
swish closed, the chorus lyric to the Faces' Ooh La La kicks in over
the top, and Wes Anderson's hitherto-somewhat-obfuscated point
suddenly comes into beautifully sharp focus.
If They'd Gone Bleak: Max would've tried to give Ms Cross the
reacharound, had his specs slapped off, and left us with the
unimaginably sour implication that he'd learned absolutely nothing
about the world or his place in it. Gah.
As their comments show, the bleak finish would have involved Max descending into his childish manner again, making an inappropriate move and thus showing nothing had changed in the film. Instead, regardless of what his true feelings are, Max contains himself and we are given a final reminder of his old life before his journey into the "new".
Rolling Stone magazine agree, stating:
To call Rushmore a romantic triangle about clinical depressives
doesn't allow for the film's bracing humanism. No tidy happy ending
here. Just a cotillion honoring Max's Vietnam play and allowing the
major characters to come together, change partners and dance to a
Faces song, "Ooh La La," that links youth and experience in a lovely,
fleeting moment of reconciliation before the shooting recommences.
Anderson closes the curtain on his movie as if he were directing a
play by Max Fischer, which, of course, is just what he has done.
So whilst there could be many interpretations, I feel the ending is simply the first snapshot of Max's adulthood.