Drinkin' & Drivin'
Whether it's on TV, on billboards, or in magazines, we're constantly being told that drinking and driving is a very bad idea. Apparently, BioRex hasn't got the message yet... In the opening intro for Story mode's mission 3, BioRex can be seen downing an entire bottle of booze to himself. Then, it's off to the racetrack...
A high blood alcohol level doesn't seem to affect Rex's performance though - In this right screenshot, we can see that he's leading the pack of racers.

ROB Robot...
When you race on the Port Town Aero Dive course, the track's intro shows a bit of the surrounding scenery. For a brief moment, the camera focuses on a large robot... A miniature robot just like this one was actually created in the early days of the Nintendo Entertainment System. He was known as ROB (Robotic Operating Buddy), and followed orders by players in a few games. Although ROB was a useful toy used for marketing the NES, he wasn't all that useful. He has become a somewhat valuable collector's item, however.

Thanks to Crash for the info on ROB

The Name's McCloud... James McCloud
The pilot of the Little Wyvern shares the name of another famous Nintendo character... James McCloud bears the same name as Fox McCloud's father from StarFox. Both James McClouds were fighter pilots, and leaders of their respective teams. James McCloud's machine also has a definite resemblance to that of an Arwing...

Moving Parts...
This is a detail that should have been used on more vehicles... Only two crafts in the entire game actually have visible moving parts. Samurai Goroh's Fire Stingray has a fin that's used for turning his machine, while the Rainbow Phoenix (unlocked by completing Mission 1 of Story mode on Very Hard) has wings that spread when you boost.

Forced Retirement...
After your machine has taken a severe amount of damage, you'll crash and burn. The word 'Retired' then appears on screen. This seems a bit mild, don't you think? A charred wreck such as this deserves to be called "Deceased", "Cremated", or even "Extra Crispy"...

Laser Lighting...
The GameCube logo can be found written in laser lights in a couple places within the game. You can spot a blue laser light logo in the Casino Palace, as well as a red and blue version in the background of the winner's circle on Grand Prix mode.

Need for Speed...
In mission 6 of Story mode (Black Shadow's Trap), Black Shadow restrains Captain Falcon, and straps a bomb to his racing machine... If the speed of Falcon's machine drops below a certain mark, the bomb will explode. This scenario seems a bit familiar... Almost as if it were something you'd see in a movie... Where's Keanu Reeves when you need him? (The film was 'Speed', released in 1994, and starred Keanu Reeves and Sandra Bulloch in case you have no clue as to what I'm rambling about here...)

On another note, if Black Shadow wants to eliminate Falcon so badly, why doesn't he just grab a gun and shoot him? Ah well, I suppose creating a needlessly complex and elaborate plan while giving the hero a golden opportunity to escape is what evil villains have become famous for...

Version Variations...
Just a detail from the winner's podium, where the top 3 ranking racers in the Grand Prix celebrate their victory... Circling aroundhe bottom of the platform, you can spot the words "GameCube Version". This of course is because two versions of F-Zero were released at roughly the same time; F-Zero GX made an appearance on your Nintendo GameCube, while F-Zero AX arrived at local arcades.

Arcade Action ...
In the first mission of Story mode, Captain Falcon is training with his machine on a simulated course. The track he's racing on is called 'Sonic Oval', and it can be found in F-Zero AX, the arcade counterpart to F-Zero GX. It just so happens that the seat for the F-Zero arcade looks like the Blue Falcon, and that's where Falcon is sitting where he trains.

A Frightening Sight...
It's the F-Zero TV guy's job to interview the winner in Grand Prix mode. In his line of work, he gets to meet plenty of interesting people (and aliens, cyborgs, etc...) Normally, the interview goes well... But he's terrified of several contestants. He shakes with fear as he talks to Pico, Zoda, Blood Falcon, Black Shadow and Deathborn.

Japanese Joke...
When Captain Falcon enters the race in mission 3 of Story mode (High Stakes in Mute City), he doesn't use his real name... He goes by the alias 'Famicom'. That name is actually the Japanese name for the older Nintendo systems, known as the Famicom and Super Famicom (NES and Super NES).

Scrapes and Scratches...
F-Zero racing is an incredibly fast and dangerous sport. In addition to the high speeds, crafts often deliberately smash into one other to inflict damage. At first glance, the machines look shiny and new. But upon close inspection, you'll be able to notice the scars that these machines bear from aggressive racing. Here in the pilot profiles menu, we see a closeup of the marks and scratches on the Red Gazelle.

Creators of the Universe
In the final chapter of story mode, Captain Falcon is challenged by the Creators of the Universe... In this mission, he races against a 'Staff Ghost'. By racing against a 'Staff Ghost', the developers are implying that they Created the Universe... Well, the F-Zero universe, anyway...

Turtle Twist...
Another 'coincidental' naming scheme... After completing mission 3 of story mode (High Stakes in Mute City) on Very Hard difficulty, you'll unlock a machine called the Rolling Turtle, weighing in at 999 kg. The pilot is a robot known as QQQ. The 'joke', is that 'QQQ' looks almost like 999, the weight of his machine.

It's kinda strange how anyone would choose to name a racing machine after such a slow creature, especially when other machines have fast animal names like 'Red Gazelle', 'Iron Tiger', and 'Bunny Flash'...