Nanny McDead - S1-E2
Stupidity: Mrs. Peterson tells the cops in the first interview that the phone went 'straight to voicemail', which would happen if the phone was off, and it's not the case. There's no reason why she'd lie about this particular fact. Which ties into the larger problem that the cops are looking for the missing phone but nobody tried to call it nor the phone company told them it was still on, or the plot wouldn't work.
Answer: The networks are now having winter breaks. A mid season end of new episodes, when they come back after the new year, it picks up as if several months have gone by. Beckett suggested Valentine's Day as a "chick flick" to watch as she is moved in. Also some episodes are not scheduled to air in order.