The exercise room is a redress of a part of main engineering; the "pool table" was removed and mirrors were erected, one to hide the master systems display and the other at the opposite end of this part of the engineering set.
This is the first time the audience sees Deanna's love of chocolate.
The age of the character Devinoni Ral was given in his computer file as 41 which was a full decade older than the actor Matt McCoy playing him. This is common in the Star Trek universe where most character's ages are roughly 10 years above that of the actors playing them. This is to represent increases in the human life span caused by scientific & medical advances contained in Star Trek's vision of the future.
"The Price" featured what would become major plot points for two other series in the Star Trek universe. In Star Trek: Deep Space Nine (1993) a wormhole was discovered (albeit stable). Similarly, in Star Trek: Voyager (1995), a ship became lost in the Delta Quadrant.
In the scene immediately after Crusher and Troi's exercise, according to the Star Trek: The Next Generation Companion, Goss is referring to the size of his "sex organ" when he is making a revealing gesture to a Starfleet crewwoman in Ten Forward.