When Max is playing with the rubber mask to cheer up a "not grumpy" Jessie before he goes to see Goose, the baby (Sprog) in the background has different toys in his left hand each time we see him. When Max takes off the mask, Sprog has a brick, ball or similar object that he can clearly lift, and the plush toy is behind him, out of reach. When Max jumps onto the table, we see Sprog in close-up holding the barrel of Max's service revolver. Then after Jessie tells Max to "get out of here" Sprog now has the plush toy.
When Jessie walks to the car Max is repairing she is wearing sneakers. When she walks around to the passenger side of the car she has on boots with sheepskin trim. When she walks off to the beach she is wearing the deck shoes again.
In the beginning of the movie, the camera pans toward Roop while he is sitting atop the concrete wall looking through the rifle scope, it can be seen that his left pants leg is cut/damaged above the knee. Next scene he is running toward the police car, there is no damage to the pants.
When Max hears Jessie screaming when she's being chased by bikers in the woods, he grabs his rifle and runs towards here with no shoes on. In the next sequence, after Max takes a few steps towards the woods, he's wearing shoes.
When Max and Jessie first take off for their vacation, it's just the two of them (no baby). There's no baby anywhere when they're on the beach initially either. The baby first appears at the gas station, when Jessie tells Max that she's going to buy an ice cream cone.
When Max takes the black interceptor to hunt down the Toecutter and his gang, he first comes up behind them on a road with a dashed white lines in the center and the road is lined with trees on both sides. This continues for as far as the viewer's eyes can see. When he spins up the supercharger in the next scene to run down the bikers, the road has changed to one with no lines in the middle, is narrower, and has open fields on each side.
Max's shoes changes third time when he is running on the road to pick up Jessie.Early he was shoeless and then wearing black shoes as written in an above statement and again in this scene he is seen wearing another pair.
When Jesse and May are being chased in the station wagon, it quits running because of radiator failure due to a piece of the gate they drive through stuck in it. It can be seen when Jesse runs in front of the car. When Max runs by the car moments later, it is no longer visible in the radiator.
Goose starts up his cold bike in the morning and immediately races a full throttle burnout. A carburetor engine of that time is rather delicate during its cold start phase, it could not deliver that performance, but rather choke and stall when operated full throttle.
When the Holden Monaro that the Nightrider has stolen passes the camera, at close range in one scene, we can see that the exhaust tips of the car are actually just dangling on the car and aren't actually connected at all.
The goof item below may give away important plot points.
At the end of the movie, when Max finds Johnny the Boy, he puts his shotgun to Johnny's head and we hear a gun being cocked. However, Max's shotgun has no external hammers and can't be thumb-cocked. (Max could be disengaging the safety, but there are two distinct clicks instead of one.)