There is a seemingly obvious Plot Hole. When Will first heard about Peter Ward, the man whose family was killed in his house, why did he not look up the subject matter on Google, where he would have seen what Peter had looked like? He subconsciously knew that he was Peter Ward, so he wanted to avoid doing anything that would reveal that obvious fact.
When Ann came over to give Will some stew, it seemed rather rude of Libby to not come down and greet her new neighbor as well. Makes more sense when you realize Libby couldn't interact with Ann, so having her come down to talk to her would jeopardize his delusion that he crafted.