The Wolf of Wall StreetGoofs
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When Jordan and Donny talk about how Donny married his first cousin, Donny claims that there is a 60-65% chance of birth defects stemming from his first-cousin marriage. In fact, even with first cousins, the chance of birth defects occurring from an isolated cousin marriage is not significantly higher than average - an estimated 3.5-4% as opposed to 3%. Inbreeding can be a bigger problem if close relatives continue to marry each other over several generations (which is why the Spanish Habsburgs went extinct, but only after several generations of serious inbreeding, or why Pakistan - where cousin marriages are very prevalent - has a particularly serious inbreeding problem), but even in these cases the chance varies wildly from 10-40% depending on other factors. Also, autosomal recessive disorders are consequent defects that are not immediately noticeable.
Errors in geography
At the beginning of the movie, when Jordan Belfort reveals that on a daily basis he takes enough drugs to supply Manhattan, Long Island, and Queens for a month, he says that he takes Adderall to stay focused. Adderall was not released until 1996, and was not released in a generic form to the market until 2002. Given that the film spans from 1987 to sometime in the 1990's, using "prescription Amphetamine pills to focus" would be much more factually accurate and understood than using "Adderall to focus" during the 1987-1990's time span of the film.
Towards the end of the film, Jordan puts his daughter in a late model R129 Mercedes SL500 to take her away from Naomi (either a 1999 or a 2000). Not only does this car not fit the time-frame of this film, but the way he engages the parking brake in reverse (with his right hand pulling upwards) is incorrect on this type of vehicle. The parking brake is located near the brake pedal and must be pressed down with your left foot.
When Jordan is leaving the country club and crawls to the steps, the number of steps changes (dramatically increases) when viewed from Jordan's perspective and also when he rolls down them. This isn't a continuity error. Because Jordan was high on drugs his perspective of reality was affected, so to him there were more steps to navigate. Just as he later claimed to have driven home without scratching the car, when he had actually trashed it. His perspective of reality was affected by the drugs.
Incorrectly regarded as goofs
When Jordan is having a flashback to driving his Lamborghini out of the country club while high on Lemmons, we see him yank the steering wheel to the left; but in the following shot, the car moves forward and turns to the right. However, this is not a goof since Martin Scorsese has confirmed that where Jordan has taken drugs the editing becomes odd on purpose, with continuity issues to make events flow oddly.