The Enterprise hosts negotiations for possession of the only known stable wormhole.
Ten Forward’s new screensaver was excellent
First Broadcast: 13th November 1989.
Quote: “People have been doing that for thousands of years!”
Score: 6
MP3 can be downloaded here. More episode info on IMDB, Memory Alpha, and Wikipedia
Star Trek: The Rewatch 
Is it possible that the Enterprise employees nanotechnology as an invisible ship-board cleaning army? Such microscopic devices could work day and night to keep all surfaces of the ship in a state of perpetual cleanliness.
So, when Troi’s man insists on using foot-fetish grease during their private “negotiations”, the stains that they leave (all over her quarters, and the jeffries tubes, and the battle bridge, and Geordi’s quarters while he’s on duty) will have essentially vanished by the next day.
This theory might also be supported by Riker’s laughable comment from a prior season that, “The ship cleans itself.”
I imagine a lack of chairs was not the reason Picard gave up his chair. He was so eager to offer his chair to the Ferengi, I suspect he just wanted out of the conference room and away from the Ferengi.