When Castle is telling Beckett that he believes Genevieve is a genie and she wants him to be her master, Beckett is standing up straight, but leaning on the kitchen counter in the following shot.
The "seal of Solomon", as presented on the cover of the "1001 Arabian Nights" book displayed on Beckett's computer, has Hebrew text surrounding the seal, but while Hebrew is written from right to left, the text around the seal can only be read from left to right - like in English. Its not that the text is mirrored, it is just written using normal characters but in the wrong direction. Also the Hebrew text is nonsensical and sounds like a bad machine translation of something like "in your life you will never have your equal among kings".
Lainie asks if the book "1001 Arabian Nights" is a story about a misogynistic serial killer. Misogeny is the hatred of women, nothing more, so a jealous king who executes concubines to keep other men away from them is not misogynistic. He does not hate women, just the opposite.
When Richard Castle says "Genevieve is short for "genie"," the line is obviously backwards as genie would be short for Genevieve. This could be an intentional mistake to show how rattled Castle is.