Jessica's middle name is revealed to be Campbell, after her mother's maiden name. In the comics, Campbell was Jessica's original surname. She took the surname Jones later after the family that adopted her following her family's death.
The movie that Jessica and Trish are watching on the roof at the end is Touch of Evil (1958). The scene being shown is from the beginning of the movie, which is considered one of the greatest and longest single takes in cinema history.
Stirling's club was going to be called Alias, which is what Jessica later names her detective agency. Alias is also the name of the comic book this series is based upon.
The full version of the song's clip can be found on Marvel's official YouTube channel titled "I Want Your Cray Cray (Full Video)". The clip has interesting in-universe facts about the song and Trish.