At the beginning of the end credits, it says "In Loving Memory of Bob Saget" who died nine days before this pilot aired. Bob Saget was the narrator for How I Met Your Mother (2005).
Sid and Jesse's apartment is the same one that Marshall and Lily had together in How I Met Your Mother (2005).
The old married couple that Sid rented the house from were Marshall and Lily from How I Met Your Mother.
Hannah leaves her engagement party in order to perform emergency surgery, back in LA, when a lung becomes available for her patient. It would take almost 10 hours to drive from downtown New York to JFK, go through airport security, fly to LA, transfer from LAX to her hospital & change & scrub for surgery. A lung is typically only viable for a maximum of 8 hours. In reality, the transplant would have been performed by another surgeon.