I remember the first time I saw “Dirty Dancing” at a press screening twenty years ago. There was a lot of snickering at this corny romance set in a late-’50s Catskills resort. None of the cynics in that room would or could have guessed it would become an enduring cultural icon or a rite of passage for a generation of teenage girls as my colleague Mackenzie Dawson poignantly wrote recently in The Post. I moderated a panel at the Lake Placid Film Forum a few years with one of the movie’s producers, who had lined up financing from a bunch of dentists, and he said they were just as shocked at the phenomenal success of the movie, which was actually filmed in Lake Lure, North Carolina. In the film’s 20th anniversary DVD, released Tuesday, Jennifer Grey, who looked much sexier before her nose job, recalls thinking of the film as an “experiment” that no one would actually see, especially after he agent told her it was a terrible movie. Among the copious extras on the Lionsgate release is a nice tribute to Jerry Orbach, extensive interviews with Patrick Swayze and a quite salacious outtake of a bareshirted Swayze bumping-and-grinding with Gray, outfitted in bra and panties. The film’s actual anniversary, by the way, is August 21. There will be a second celebration then, when the film begins a one-week booking at the Ziegfeld.