Dr. M'Benga does the same thing with his daughter that Chief Montgomery Scott did in Relics (1992): preserve a life in the transporter buffer.
The "buildings on a bridge over water" that were depicted on Hetemit IX , are real buildings over Lake Ontario in Toronto, beside Budweiser's Stage. Based on Toronto's former "Ontario Place"
This episode was directed by Leslie Hope, who previously played Kira Nerys' mother Kira Meru in Wrongs Darker than Death or Night (1998).
The line by Pike "This place is fun. They should sell tickets," while Pike and Spock are awaiting the passage of the ion storm in the Illyrian Colony's library is a direct reference to Ontario Place's original design, from its opening in 1971 until 2012, as a family amusement park attraction which required the purchase of a ticket for admission. Still in operation is the world's first permanent IMAX theatre in the Cinesphere, which is featured in most of the external shots of the Illyrian colony.
The backstory for Una/Number One is from the book Vulcan's Glory by D.C. Fontana, a prominent Star Trek (1966) writer. This is a rare case where something that first appeared in a novel became Trek canon.