Corrected entry: When Sam gets killed and gives chase to the killer, he steps into a puddle and makes it splash.
Corrected entry: You can see Sam's shadow the whole time.
Correction: True, WE can see Sam's shadow, because we can also see Sam. But no-one else can see his shadow. So this isn't a mistake as such.
Corrected entry: At the end, after Sam moves the penny to convince Molly that Oda Mae is telling the truth, they all go into the apartment. Now, knowing that a murderer, Carl, is on his way to come and get them, you would think they would all get out of there as soon as possible. Instead, they wait around until Carl shows up, and then act all surprised and run when he gets there.
Correction: They're waiting for the police to arrive. Molly calls the sergeant just before Sam takes Oda May's body.
As Carl had told Sam of his intent to kill Molly if he did not get the money, why did Sam, Molly, and Oda Mae remain in the apartment and risk Carl's arriving before the police arrive?
I have to agree. Carl stated that if he doesn't get the money by 11:00, that he would kill Molly so it makes no sense to stay in the apartment at all. It would be much safer and smarter to go straight to the police and tell them everything.
Corrected entry: In one of the last scenes, Oda Mae, Sam and Molly are at Molly's house, waiting for the police. By now Sam has learned to touch things and people. But he does not seem to be able to touch Molly and needs to borrow the body of Oda Mae to touch Molly and dance with her.
Correction: He needs to borrow Oda Mae's body so that Molly can feel him, not the other way around.
He punches Carl, so he is able to let others feel him. Why can't he do that with Molly?
No. He says "I'd give anything if I could just touch you." That is why Oda Mae let him enter her.
Corrected entry: Willy gets inside Molly's apartment very quickly after Carl gets her to go out and take a walk with him. He's unable to get what he came for, and then goes straight to his house, where he contacts somebody on the phone - it can only be Carl. His explanation for why he couldn't get it? "She came home." But since it can only be Carl he was talking to (this is made clear by Carl's visiting Willy later on) Carl knew perfectly well that Molly came home. It's Carl that Molly was with - he'd have known full well that she left his company.
Correction: He made the puddle splash because he was probably so angry at the killer that he made the water move without realising it. He is capable of moving things, he just doesn't know how he does it yet.