In honor of its belated home video release, I searched for evidence of a theatrical one-sheet for Ladies and Gentlemen, the Fabulous Stains. I came up empty in that search, but in its place I have a scan of the small ad that New York's Film Forum placed in the Times for the film's week-long run in March of 1985. As has been well-documented in other places, the film was produced by Paramount in 1981 and promptly shelved. It gained a sizable cult audience through screenings on cable outlets such as USA (as part of the channel's Night Flight series). Over the years, there were also occasional film festival screenings. In 1985, the film had its one "official" theatrical release, beginning in New York at the Film Forum and moving onto Chicago's Facets. It had a standard one week engagement at the Film Forum and then a similar engagement at Facets in late April and early May of '85. Since it was such a specialized release, it appears that Paramount did not produce a one-sheet.
Interestingly, Paramount did produce a theatrical trailer (I wonder if it was ever actually used at public screenings in 1981 prior to the film's shelving). It unfortunately does not appear on the new Rhino DVD, but it can be viewed via their website and YouTube. I can only imagine that the exclusion of the trailer on DVD might have something to do with music rights:
In a final twist, at the last moment, Rhino's plans to simultaneously release the soundtrack were scuttled in a rights dispute with Paramount. Rhino had planned a vinyl and digital release. It was up for pre-order on the site and the songs were briefly available for download on Amazon, but quickly taken down. I imagine there's a warehouse full of Fabulous Stains vinyl somewhere. A poster at Home Theater Forum shared this information, which came from a staffer at Rhino, and the word from Paramount is that there will be no subsequent soundtrack release.