The entire movie is the mole hunt.
A very elaborate one. Kittridge suspects Phelps from the beginning. Ethan is sent into uncover the mole. The murders of the team were not expected, but prepared for by having the second IMF team around in case something happened. The scene in the restaurant, the arrest of Ethan's parents, and the CIA invasion were staged to make Phelps think they were off his trail. Ethan was genuinely surprised by Claire at the beginning. The fact that she survived causes him to think she is in league with Jim, though he wants to not believe this. We see later that, as soon as he sees Jim and listens to him accuse Kittridge, he instead envisions Jim as the villain. He even suspects Claire for a moment. Kittridge does not seem surprised upon seeing Phelps alive, even though Ethan never said anything to prepare him for this.
- Consider how during the scene at the aquarium restaurant, nobody in the room makes any effort to notice or prevent Ethan from unwrapping his explosive gum. It seems out of character for IMF agents to have this lack of observation skill, but it's unlikely they'd let him pull this sleight of hand if they really were trying to apprehend a mole. The gum exploding gum is shown later in the film to be survivable so the waiter who was Blown Across the Room probably survived. Oddly, nobody even slightly attempts to chase after Ethan after he ruptures the aquarium and flees the water flooding the place.
John Voight's Jim Phelps is not the real Phelps.
He's a rogue SYNDICATE agent that killed the real Jim (Peter Graves) and took his place. He decided that both the masquerade and his loyalty to the SYNDICATE are through, so he decides to be a mole for hire.
- Alternatively, he could be an IMF agent who was brought in to take on the role of the 'original' Jim Phelps after the real one retired (much like some fan theories that the different James Bond actors represent different agents who are given the same name and agent number to increase Bond's reputation).
- There's actually a fanfic based on this very premise- "The Oldest Trick in the Book"- where Ethan is visited by Cinnamon Carter at the funeral of the 'fake' Jim Phelps and learns the man's real history; the fic even concludes with the real Jim acknowledging Ethan as the future of the agency.
If this is true, it would be yet another reason why the exact nature of the Rabbit's Foot was kept unclear. It could probably be considered offensive for the film to feature a Chinese bioweapon that targets white people.
...because there are more countries to recover lost episodes from, and presumably more prints were made.
The Rabbit's Foot is the Luck Virus.
The MI movies take place in the Red Dwarf
universe. The Rabbit's Foot in MI:3 is a prototype Luck Virus. Untested. Dangerous stuff. Ethan Hunt is probably infected already. The virus may even be collected from the cells of top MI agents.
The real mole in the first movie was Dan Briggs
Briggs saved the world more times in one year than James Bond
does in a good decade, and how did the IMF repay him? They took his team away and gave it to Jim Phelps. What's more, his teammates never so much as spoke of him ever again. The first movie was his plot to destroy the IMF in general and Phelps in particular.
The Svardians are descended from the children of Hamelin and of an English town; that's why the language is the way it is.
Jon Voight's Jim Phelps is really the son of Peter Graves' Jim Phelps, James Phelps Jr.
Given Voight looks middle aged in contrast to Graves around the time being a senior and how Voight during in his acting was around his twenties and too young to serve in the Korean War which Graves' Phelps has. There could be a lot more to the film's Phelps choosing to betray the IMF and of why he was disillusioned. Voight's Phelps Junior could be The Vietnam Vet
during the timeframe of the television when his father the Jim Phelps portrayed by Graves was doing missions, initially a "Well Done, Son!" Guy
wanting to follow his footsteps of his father by first serving in Vietnam just like how Graves' Phelps started out by serving in Korea prior to joining the IMF. However, unlike Graves' Phelps who kept his idealism and patriotism throughout the series, Voight's Phelps may have being planted with cynicism upon seeing unmentionable War Is Hell
horrors committed by both sides and eventually how the conflict itself resulted in America losing the war and Voight's character being seen and treated as a figure of hate for his service to begin with, turned him into a Shell-Shocked Veteran
who would gradually undergo Sanity Slippage
that would eventually serve as the true catalyst for his villainy in the first film. Voight's Phelps would join the IMF as a means to exorcise his traumatic demons by living up to his father and upholding operations elsewhere outside of Graves' Phelps' missions shown in episodes of both the original and the 1988 series, but likely developed a Inferiority Superiority Complex
for being in the shadow of Graves' Phelps and may have started to resent the IMF for favoring his father over him even during service. It's only after feeling disillusioned with his efforts it has exacerbated his cynical 'Nam-dated mindset, his insecurity of his inability to truly measure up to his legendary father and warped traumatized mentality he goes totally insane and pulls a FaceHeel Turn
as "Job," becoming an Evil Counterpart
to Graves' Phelps and an Antagonistic Offspring
determined to destroyed his own father's legacy out of blaming his celebrated experience and unwittingly putting him permanently under his shadow for make him feel worthless that exacerbated his choice to go bad as a means to escape Graves' Phelps' shadow.