When they show shots of any of the angels, they rarely blink. Nicolas Cage actually practiced not blinking and was able to do it for several minutes by the time the film was done. However, once he became human he was able to blink all he wanted.
When Seth falls to Earth appear pictures from his memory in black and white. It is because due his condition of angel, Seth can't see or distinguish the colors. It's a nod to Wings of Desire (1987) (1987), where the angels was unable to see in colors.
During the opening sequence, you see 3 angels on top of a building as the camera pans up and around and you see the building's number, 444. 444 is a direct reference to the angelic realm: "Thousands of angels surround you at this moment, loving and supporting you. You have a very strong and clear connection with the angelic realm, and are an Earth angel yourself. You have nothing to fear - all is well."
The concept of angels moving among the living, hearing their conversations, experiencing beauty that humans rarely stop to enjoy or even notice, yet not feeling any emotion or passing any judgment, was first discussed in the writings of Rainer Maria Rilke, specifically, his collection "The Duino Elegies".
This dialogue between Seth (Nicolas Cage) and Maggie - "Let's go." "Where?" "I don't care." "What will we do?" "Anything." - is virtually identical to an exchange between Cage and Deborah Foreman in Valley Girl (1983).
When Seth becomes human, he can only understand the English language. This is the opposite to Wings of Desire (1987), where Damiel (Bruno Ganz) can speak any language after the fall to Earth and becoming human.
When Meg Ryan is looking in the mirror and Nicolas Cage is not reflected, this was shot twice with motion control: once with Ryan and Cage, once without the actors, and mixed together. also, if you look closely enough, you can see a few strands of Ryan's hair morphing in and out where Cage's face was erased.
The sequence in the library with an old man reading a Hemingway's book is a nod to the Wings of Desire (1987). In it Curt Bois plays Homer, an aged poet that his poethical thoughts are read by Damiel some times.
Although the movie show some important places of Los Angeles' city like Terminal Annex, Mulholland Drive, Los Angeles International Airport, Grand Central Market or Dodger Stadium, the library by where the angels walk is located in San Francisco.
The trivia item below may give away important plot points.
The film shares many parallels and similarities to Hans Christian Andersen's 1837 short story, "The Little Mermaid." Both stories are about mystical beings who dream of becoming human after meeting and falling in love with one on earth. After repeated warnings from those around them, both protagonists find a way to become human and be with the one they love. Both end up losing their love shortly after, and, although grief-stricken, both feel hopeful for their futures that their new-found humanity has brought them.