I think one of the strengths of the 2nd part of this film is that her actions -don't- come across as "creepy" or "stalkerish," because they very well could have been.
Part of it is just for simplistic reasons. She's not breaking in to create a collection of his toenail clippings or to spy on him or smell his clothes or something.
Part of it is because of Wong's character and acting. The act of her breaking in is sad or pitiable or even romantic well before it's "stalkerish." She doesn't do it because she's obsessed; she does it because shes lonely. When she's in the apartment, she's not somber or serious or crying that she's not with this man; she's aloof and happy for once because when she's able to make someone else happy, even if that person don't know who's doing(or why they've suddenly been sleeping better and tasting food better).
Obviously I'm not saying breaking into a person's apartment is a completely normal or moral thing to do, but I think her motives are pure, rather than obsessive or perverse, and that distinction makes a big difference. It doesn't make her a completely balanced individual; it doesn't excuse her, but it explains her.
I also think there's at least to a tiny degree a culture shift that's happened in the last ten years or so, largely because of the internet and social networks. I can think of countless scenes and scenarios from books and movies and TV shows from the past of people not giving up on loved ones or doing extremely thoughtful acts that were at the time considered heart-achingly romantic; today, they'd be considered "obsessive" or "creepy."
I disagree. I thought her actions were creepy and stalkerish. She snuck into his house before she had even had a conversation with him and she searched his bed for another woman's hair. That's creepy.
Yes, I thought it was stalkerish. Fans of Faye dismiss it as acceptable 'cuz they find her to be cute & adorkable but let's face it, she was a stalker. Just because she didn't do anything super nutso doesn't make what she did any more acceptable. She was breaking the law by breaking into that cop's apartment - how ironic is that?
As for why the cop didn't notice, I think he was so depressed over losing his ex that he wasn't noticing the changes in his apartment, esp. since they were very subtle. Plus he was a beat cop, not a detective, lol. JK about that last part; I think it was his romantic funk/depression that caused him not to notice stuff.