The background logo at the beginning of each session excerpt is, presumably, the logo of The Academy, which is revealed in these sessions to be where young River was being held and educated by the Alliance.

River's favorite class is Physics, of which she was already in the graduate program.

River's fellow students at the Academy called her Little Mouse.

River tells the interviewer that Simon has said she has the "third eye". This is a term used to describe the intuition or clairvoyance of certain people who seem to know things about others without being told, or of knowing the future.

River explains to the interviewer that Simon is a trauma surgeon in Capital City. This is the capital of Osiris, one of the wealthy central worlds of the Alliance.

The interviewer remarks that Dr. Mathias is proud of River's progress in the Academy. We don't see the doctor here, but we later will witness his death (unnamed) at the hands of the Operative in the movie Serenity.

River mentions the Pax. This is a shorthand name for G-23 Paxilon Hydrochlorate, a chemical compound that has been used by the Alliance to pacify the citizens, effective on 99.9% of individuals (the other .1% become Reavers, as revealed in the movie Serenity).

River makes a comment about finding a pea under 20 mattresses "and you wonder why I'm not sleeping?" This is a reference to the fairy tale "The Princess and the Pea" by Hans Christian Andersen about a princess whose royal identity is proven when she feels an uncomfortable lump while trying to sleep on a stack of 20 mattresses lying upon a pea.

Memorable Dialog

they call me Little Mouse.wav 

would I still be allowed to dance.wav

I can see you.wav