OK, we can (with a reasonable degree of certainty) recreate the music George Washington had on his walkman. Musical notation is fairly static and so we have copies of sheet music from the 1700s.
Do we know how he danced? There is (I think) no system of dance notation. Even a reasonably complex dance seems impossible to describe in a compact written form.
Therefore, how certain are we about the dances done in the times before film images?
There is a system of dance notation, as has been pointed out by The Master: http://www.straightdope.com/classics/a1_389a.html
Dances created before this time were no doubt passed down in a manner akin to oral tradition. Geo. Washington was probably taught by an older relative or friend, and he saw to it that his step children and grandchildren were taught in a like manner.
So we can say that any movie showing ol wooden teeth doing the Mashed Potato is not as historically accurate as I woulld have hoped?
The image of the father of our country dancing is one that most self-respecting publishers of history books would do well to exorcise. However, there is one )unconfirmed) report of Mr. Washington doing the Twist. That picture may be found in a publication such as The Onion. However, it is more likely to be found in the new book 100 Years Of The National Enquirer, complete with headline “Father of country was a real party animal”. Of course that is something that is likely to be disputed by the Washington estate. Same as with the pictures of George F Will doing the Macarena.
Music (and therefore dance style) must be timeless! Have none of you seen the epic movie A Knight’s Tale? Why, back then they were jousting to “WE Will Rock You” and partying to “You Shook Me All Night Long”. 'Nuff Said. 
Paul, your question seems to have been answered. I’ll add this quote from “Dance Music from Three Centuries”
“George Washington . . . was very fond of dancing, especially the Minuet.”
It describes the minuet:
“It is in triple time, leisurely and gracious”.
From the beat and the tempo, at least, we can assume they weren’t doing the twist.