While in Atlantic City, Randy tells Jack that she's 19, but you need to be 21 to legally gamble and when she cashes her paycheck at the Casino after showing her I.D., the teller would have discovered that she was underage and wouldn't have been able to give the chips to play table games.
During the most of the movie, Randy wears a blouse is buttoned up to the neck and a necklace over the top of it. Except for the scene where she is exiting the casino after her big loss, as she walks out and her blouse is unbuttoned at the neck and she is not wearing the necklace. However, in the next scene the blouse is buttoned again and necklace returns.
The description of an apparent discontinuity is accurate; however, in the shot with open blouse and sans necklace, Randy is also not wearing her jacket. In the following shot, as she emerges from the casino with Jack after her devastating setback, she has donned her jacket, buttoned her blouse, and restored her necklace. The apparent costume discontinuity dissolves in the brief lapse of unrecorded time.
At the 53 minute mark, when Jack (Robert Downey Jr) & Phill (Danny Aiello) are parked at a traffic light, it's VERY CLEARLY two stunt doubles.
In the movie's final scene, Randi (Molly Ringwald) appears outside Jack's (Robert Downey Jr.) Home as Jack emerges. But Randi should have no idea where Jack lives, and the home belongs to his grandmother so he can't look it up.
When Randy leads Jack and a group of kids on a tour of the museum, she and the kids refer to a dinosaur as a 'Brontosaurus.' By the 1980s it was already well known that the correct name for this animal is 'Apatosaurus.' A tour guide should know this.