Thad knows (as do most people within earshot) how much I love Artists and Models, so I thank him profusely for uploading the trailer after he bought a copy off ebay; here's his own post about it.
As he notes, and as you can see below, the trailer doesn't really tell you much about the film. Most trailers try to oversell the story, but this does the exact opposite, leaving out most of the satire and all the crazy Cold War spy stuff from the last third. It even soft-pedals the film's status as a cheesecake calendar come to life, which you'd think would be the absolute first thing a trailer would want to play up -- but to do that, they would have had to include Eva Gabor in there, and she only appears once the spy plot starts up.
It makes me wonder if the missing plot points from the spy section, which I've written about before, might be a sign that they weren't even sure about including that part in the movie at all. With a few reshoots it would actually have been possible to create a different ending for the picture (maybe right after the title number at the ball). Or maybe not.
But I do get the impression the studio -- or Wallis -- thought the movie's weaknesses were concentrated in that final section, which would explain why it was allowed to go with several sequences written but not shot, and why it doesn't appear in the trailer. Many people agree that the movie falls apart once the spies come in, so they wouldn't have been far out if they had believed this, but I personally feel like the "fever dream" aspect of the film is enhanced by the fact that it gets crazier as it goes on, until by the end it resembles one of the nonsensical comic books that have destroyed Jerry Lewis's mind. That steadily increasing lunacy, after starting like a sort-of-normal Martin and Lewis movie, is one of the things that made it so influential for the French New Wave.
The trailer doesn't include any "outtakes" either - none of Shirley MacLaine's "The Bat Lady" number, which was described in some of the publicity (she was supposed to do it while "flying" on wires) but never seen, and possibly never shot at all. As I said, it's a long movie and it was over budget, despite being part of a series that was supposed to turn a big profit on relatively small investments (like Wallis's later series of Elvis movies, though those were even cheaper). It might be that they just ran out of money or time and pulled the plug on that musical number, as well as various plot points.