Blondes the daughter's necklace - he took that from Sarah Kay's house after he killed her, and gave it to the daughter. He's always been bizarrely cocky and reckless (I think the train conversation in S2E1 fits with that). Plus it was an odd gift, heavy and dated, not what you'd expect a little girl to have. Sally's mother commented on it.
Cadbury I didn't think the police would give a name, but perhaps say they were being helped by someone who had had X experience, something like that. Or others may be right, it may be that she was the only one he used the name Peter with, or the efit pointed to her (was that released before his failed attack on the last victim? because he knows that she lived) or a combination.
I did feel a difference between this episode and the last series, it was far less tightly drawn, and I found lots of it hard to believe, especially the scene with the babysitter. It did feel a little in the realm of the absurd.
But I wonder if that's supposed to reflect how much his wheels are coming off. In the first series he was painted as a personable guy who likes to kill women. Now he's so menacing, and volatile.... just a total maniac.
I'm so interested to know how she catches him - she will, surely.