Kirk says "It looks like New York City." La'an responds "It's Toronto." This is an allusion to the fact that Toronto is often filmed as a stand-in for New York City in many shows and films.
Kirk mispronounces La'an's surname as "Noonien-Soong". Dr Noonien Soong is the cyberneticist who created Data (and Lore and B-4) in Star Trek: The Next Generation (1987). Dr. Soong also has ancestors (in the 21st and 22nd Centuries) that were involved with Eugenics and Augments (i.e., Khan Noonien Singh who is La'an's ancestor.
The painting that Pelia is accused of stealing from the Louvre is "The Concert by an open window" by Johannes Vermeer, also known as the Concert.
In this time line where Kirk was not born on Earth, but on a starship (the USS Iowa), Kirk exclaims the line "I'm from space!" This echos Kirk's line from Star Trek IV: The Voyage Home "No, I'm from Iowa. I only work in outer space."
Pelia, portrayed by Carol Kane, tries to brush off La'an Noonien-Singh and James T. Kirk by saying, "We're closed!" In "The Princess Bride" (1987), Carol Kane played Valerie, wife of Miracle Max, who tried to brush off Iñigo and Fezzik with the same line.