Visible crew/equipment: In the shot where Austin is on the bed with the twins, the one on Austin's left lifts up her ankle on the bed. There is a cable visibly stuck on her shoe. It slips off after about a second.
Continuity mistake: Just after Nigel and Austin are turned around on the bed to face Goldmember, we see Foxxy filing Goldmember's nails from behind. In the very next shot where we see the front of Goldmember his nails are still being filed, but then in the next shot Foxxy is simply standing there and Goldmember sitting still as if they were doing nothing. (00:29:15)
Deliberate mistake: Basil tells Austin he is being sent to Studio 69 located on Eighth Avenue and 69th Street in New York City. However there is no such address. Eighth Avenue ends at 59th Street, after that it becomes Columbus Avenue.
Factual error: If you look closely at the bar in the club when Austin goes back in time, there is a bottle of Tangerey "Ten": a gin only recently introduced, so it would not be around in the '70s. (00:23:51)
Factual error: After Fat Bastard's sumo match he goes to the toilet -- a Western style toilet. The sumo arena, especially the locker room area, would be traditionally Japanese. There is no way that a Western style, sit down toilet would be found there. What we should see is a silhouette of Fat Bastard squatting down over a Japanese style toilet which is like a trough in the floor. (00:48:00)
Plot hole: How can Austin's Father be so young? Don't forget that Austin was frozen for 30 years, so their age gap should be 30 more than normal; but despite that the age gap between them seems about normal for a father and son.
Continuity mistake: When Austin and Foxy are in the time machine leaving the club about to travel to 2002, Foxy is wearing large gold hoop earrings, but after the first shot she only has one earring in (the left ear).
Continuity mistake: When Austin kicks Mini Me, the knife and envelope are dropped under him. Two shots later, the knife is still there but the envelope has vanished.