The Wachowskis embedded so many layers of symbolism into their cult film trilogy, people are still uncovering secrets in the Matrix movies decades later. The first installment - released in 1999 - is particularly rife with Easter eggs; visual, verbal, and audible clues all hint at themes and key plot points from the second and third films in the trilogy.
These secrets are buried with mixed degrees of subtlety. Christian allegories are laid thick, from biblical-inspired names like Trinity, the Nebuchadnezzar ship, and the human city of Zion, to Neo basically becoming Jesus in a trench coat (his journey of death, rebirth, and acquiring miraculous powers parallels the son of God's). If that isn't enough Matrix fan theory fodder, Neo's status as "the One" is also hinted at from the very start, since his name is an anagram of the word.
While you might have picked up on some of the more obvious homages (like when Trinity tells Neo to "follow the white rabbit,") there's lots of other foreshadowing you probably missed in The Matrix.
As Neo's boss chastises the hero for being late to work in the first movie, he looks over at the office window which is covered in specks of soap. The suds are then wiped away by a window cleaner to reveal a clearer view of the room. Many astute viewers reckon - as nothing in these movies happens by chance - the soap pattern on the window represents the scrawling green lines of code Neo's world is secretly constructed out of.
Redditor /u/VonAether also pointed out, "the sound effect used for the squeegee on the window was used again later when Neo was getting sucked out of his pod in the power plant, hinting that even early in the movie he's trying to wake up."
Although Neo has little interest in his boss's lectures, some of Reinhardt's lines hold great future significance. Take for example:
You have a problem with authority, Mr. Anderson. You believe that you are special, that somehow the rules do not apply to you... The time has come to make a choice, Mr. Anderson.
Neo's "problem with authority" underscores his rebellious streak and encourages him to eventually break just about every "rule" the Matrix has set in place (he can fly, dodge bullets, etc.). Like Neo's boss, Morpheus also believes Neo is "special," and his faith is rewarded by the end of the trilogy.
While Reinhardt's arrogant tone may undermine his clairvoyance, he is right. Neo does have to make a choice: the blue pill, to remain in the virtual world, or the red pill, to wake up in reality.
During the scene in which Neo hands off a computer file to Choi, eagle-eyed viewers can make out the title of the hollowed-out book Neo hides his contraband in, Simulacra & Simulation. This alone is an obvious peek behind the digital veil of the world he currently lives in, but it's also an academic reference.
The book is real, written by French philosopher Jean Baudrillard, with the title referring to Baudrillard's theory that the modern world has become a "hyperreality" in which it's increasingly hard to distinguish the real from the virtual. To vastly oversimplify a complex idea, this is basically how humans experience the internet. Morpheus even quotes Baudrillard later on when he describes the Matrix as a "desert of the real."
For the most part, Oracle speaks in too many riddles for viewers to get a grip on future hints she might be dropping. This exchange, however, takes place when Neo first meets her, and it's pretty explicit:
Oracle: "Sorry kid, it looks like you've got the gift but it looks like you're waiting for something."
Oracle: "Your next life maybe, who knows."
Viewers don't learn the significance of Oracle's last comment until Neo reaches the Architect at the end of The Matrix: Reloaded. Once he arrives, the Architect reveals several versions of the Matrix have existed before, complete with multiple variants of Neo.