Character mistake: The killer's motive for the murder is getting kicked out of the band akin to Beatles drummer Pete Best, and Castle whispers to the camera that bass player Stu Sutcliffe would have been a more appropriate comparison. Sutcliffe quietly quit the Beatles voluntarily, while Best was fired, with his dismissal becoming widely-known public knowledge, so the comparison to Best actually is more applicable.
Character mistake: Beckett identifies the area given for the Skype call as the whole city of Paris. It's hard to believe that Beckett knows the area of a foreign city by heart, the problem is also that she is wrong. Paris actually has an area of about 105 km² (41 sq mi).
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.