Max's eyes are different; the pupil in his left eye is permanently dilated. This is a nod to Mad Max 2: The Road Warrior (1981): When his car is forced off the road by Wez and Max crashes, he suffers a severe injury to, among other body parts, his left eye. The disparity is easier to see in close-ups, and VERY easy to see in HD versions of the film. In the regular version, it's most prominent when Max first looks down on the Thunderdome.
George Miller lost interest in the project after his friend and producer Byron Kennedy was killed in a helicopter crash while location scouting. That may explain why Miller only handled the action scenes while George Ogilvie handled the rest. The film is dedicated to Byron Kennedy.
Originally, the film was supposed to be about a group of children living without parents in the wild. They were trying to decide what adult character would find them, when someone thought of Max. After that suggestion, it became a "Mad Max" film.
The sandstorm at the end of the film was real, and a camera plane actually did fly into it for some shots. The storm in its entirety hit the crew in the desert, forcing them to ride it out in their cars and wherever they could find cover.
In interviews about Mad Max 2: The Road Warrior (1981) (a.k.a. "The Road Warrior"), George Miller said that while Max's world was after the collapse of the social/political/economic system we know, it was not post-World War III. However, "Beyond Thunderdome" explicitly contradicts this.
Jedidiah's airplane is a Transavia PL-12 'Airtruk', a single-engine agricultural biplane designed by Transavia in Australia. First flown in 1965, around 120 had been built by the time this movie was made.
The script called for Aunt Entity (Tina Turner) to drive a vehicle. All of the vehicles were built using manual transmissions, which Turner couldn't drive, so a car equipped with an automatic transmission had to be constructed.
It is a popular misbelief that the vehicle Max is seen driving at the beginning and end of the film is based on a Ford F150 pick-up truck. However a modified early to mid 70's model Australian Ford Fairlane ZF-ZG was used as the base vehicle. Although the exterior of the car has been heavily modified, the vehicle is identified through the remaining pieces of the cars interior. These include a curved dashboard and ignition switch along with steering column positioning (common style of Australian Ford model's between the years 1971 to 1976,) Along with the a ZG seat trim and steering wheel. This can be confirmed through close-ups of the interior during the final chase sequence. The ZG Fairlane shares a very similar body style, chassis and engine (351, 5.8 liter V8 Cleveland) to Max's original yellow Interceptor used in "Mad Max". Making all three of the main vehicles used by Max in each film a similar variation of each other (Australian Model Ford V8, mid 70's Sedan,Coupe).
The trivia item below may give away important plot points.
Two scenes were cut from the film to bring down the running time. One where he dreams of his murdered wife and son, wakes up and cries. He realises he's become just as bad as the animals he used to hunt down as a cop. The other is Max takes a dying Gekko to the top of a sand dune at night, sees the lights of Bartertown and tells him they've reached Tomorrow-Morrow Land. A few seconds of this scene are included in the music video for Turner's "We Don't Need Another Hero".