I definitely felt some scenes were put in a little gratuitously, like the pushing the freezer scene. It made me uncomfortable, but it was more to do with the obviousness of the writer's intent. I don't agree that Castle and Beckett have an innocent relationship.
I have no issue with Beckett getting this case, at the point that they were captured, all they knew is that there had been a homicide. You can't send a case to the right department if you are missing some of the information.
But the main reason I came on here was to highlight an entertaining mistake. Right at the end Beckett removes her jacket only to have Castle promptly help her put it back on. I'm guessing they filmed the previous scene with it on forgetting that they needed it off for the next scene, but it gave me a giggle.