On a second viewing of the remake, it becomes obvious that the first time the alarm system goes off (initially shrugged off as human error) is likely the first time the Stranger enters the house.
How is Tiffany able to enter the house without setting off the alarm? Jill disabled it earlier after it went off and forgot to reset it. In addition, notice that, later on, Jill remembers to reset it. Unfortunately, the Stranger is, unbeknownst to her (and the audience, at this stage) inside the house, so the alarm system won't be of any help whatsoever...
Rosa disappears from inside the atrium early on, leaving the bird food, and Jill assumes she either went out or went to another part of the house. Later, Jill discovers Rosa's corpse in the water. She'd been killed right under Jill's nose not long after first meeting her.
In the original, the kids are stated to have been hacked apart, and Stacey, the babysitter murdered at the beginning of the remake, was apparently subjected to such a gruesome death that her remains have to be carried away in several small body bags. This comes shortly after the revelation that there was no murder weapon. The Stranger is apparently so strong he has no need for one - and he never once tries to use any weapon other than his bare hands when he attacks Jill. Just imagine what he could have done to her had she not escaped...
In the remake, after Jill puts the "phone-tapping" plan into operation, the Stranger phones three times. On his first call, he hangs up just before 60 seconds is up. The second time, he does stay on the line long enough... on the line that isn't being tapped. The third time, he stays on the correct line for a lot longer, which leads to The Reveal. On a second viewing, it becomes obvious that he's doing all of this deliberately: to lure Jill to the guest house, to get her hopes up and then dash them, and then finally to make it clear that he's been in the house the whole time - just to mess with her.
