Audio problem: When the children run out of the garden, the girl is screaming, but her mouth is not open.
Continuity mistake: When Jill puts the piece of paper with the code for the security system on top of the system in another scene it's gone, and when she returns it's back again.
Continuity mistake: When the Mandrakises were about to leave for dinner, Dr Mandrakis opens the door then goes back to activate the alarm system behind the door. In between shots, the door goes from open to closed magically.
Continuity mistake: When Jill first arrives at the house, Mrs. Mandrakis shows Jill the emergency contact numbers on the refrigerator. Rosa's last name is spelled "Rimmerrez" in this scene. Later in the movie when Jill goes back to the kitchen to get the number from the same list, Rosa's last name is now spelled Ramirez. (00:14:00 - 00:46:45)
Other mistake: After the stranger calls Jill in the guest house, she celebrates the fact that she kept him on the line for longer than a minute. However, this conversation was significantly shorter than their last, and in reality it only clocks in at around twenty seconds.
Continuity mistake: At the school lockers, Jill is seen ripping off a sticker from the back of her phone in close up. In the next shot, she is seen ripping it off again.
Continuity mistake: At the end of the movie, when Jill is in the hospital and the balloon pops, there are only two balloons: the one that popped and a mylar balloon. In the next shot there are about five mylar balloons. A few shots later there are only three mylar balloons, and at the very end there are five again.
Continuity mistake: When Jill is talking with her friend Scarlet, Scarlet's knee is occasionally up in the view, and then she is sitting normal and the sitting position changes.
Answer: The stranger could not have followed Jill to the house because when Jill gets there, he is already at the house. The front door was open. As to the second part of your question: dumb luck. The stranger was hanging out at the guest house just waiting for the parents to leave.
ChristmasJonesfan
I think he might have been stalking Jill. He could have been following her around her home and school. He targets teenage girls and might have been looking for the right moment to strike. For all we know, he broke into her house when no-one was there and could have found the address and maybe a note reminding Jill that she had to babysit, and then he just would get out there ahead of time to wait for her.