The roo-shooter's camo-painted jeep has its "OEM" headlights turn off when the windshield is shattered, yet in the next shots of the truck backing up swiftly, both the headlights and the "add-ons" are all blazing brightly again.
As Mick is leaving the hotel towards the end, he has a brief conversation with Irving the doorman. After parting, Irving is seen brandishing Mick's knife as if it had just been given to him by Mick. This is missing from their conversation.
When Sue goes down to the water to fill her canteen, the reptile that lunges forward is not a crocodile, but a large American alligator, evident by the blunt snout and the placement of the teeth when its mouth is closed. A crocodile snout is narrower and more pointed.
When Mick shoots the spotlight used by the city cowboys, the bullet is stopped by the light. The caliber of rifle that Mick uses would ensure the bullet goes through the light and into the person holding it.
Mick enters the subway at the 59th Street-Columbus Circle Station but the wall tiles feature the number 9. The scene was filmed at the 9th Avenue station on the BMT Culver Line.
At a little over the 22 minute mark, the "Sue Charlton" character asks if the King Brown snake is poisonous and "Crocodile" Dundee replies yes. This is not accurate: the snake is in fact venomous. The difference between the two is that venomous organisms inject toxins, where as poisonous ones release toxins if ingested.
Sue looks to be wearing light sand shoes. Given the harsh conditions of the Northern Territory bush and swamp lands, you would want to wear decent boots that give good foot protection and support, not light sand shoes that would fall apart and have no protection at all.
Mick tells Sue he has no idea how old he is and knows nothing about when he was born, except that it was "in the summertime". Mick later travels to New York with Sue and to get a passport, he would have had to know his birth date. EDIT: This isn't correct. It's possible for someone from Australia to obtain a passport without their birth being registered. Details of this can be found on the Australia gov't passport website under "What if my birth in Australia wasn't registered?"
In the opening credits, the cockpit of the helicopter is shown. The pilot is wearing a ball cap that says "Hiller Helicopters". The helicopter is actually a Bell Helicopter Model 47-G. Hiller did make a similar helicopter, the Hiller Model 360. The Model 360 was designated by the company as the UH-12.
EDIT: There's no mistake here. Just because someone wears an item of clothing with a logo/phrase on it doesn't mean they are associated with it.
The barrel glint of Mick's long rifle is clearly visible in front of and to the right side of the kangaroo when lit up by the drunken hunters' spotlights ("Wait! It's got a GUN!"). Yet the puff of gunsmoke does not come from the rifle. It emits from a smoke bomb placed on the kangaroo's left side.
About 45 seconds into the roo-shooting scene, an obviously fake mannequin of a kangaroo (it never moves and is sitting upright, whereas the live kangaroos are all loping away from the noisy mayhem) can be seen at the left of the picture.
Right after Crocodile Dundee climbs up to walk over the crowd in the subway station, the platform used to assist him in walking is briefly visible.