"Alexis is seen using the delete key on her laptop, a Macbook. Macs do not have a delete key, only a backspace key." MacBooks have a key labeled delete which is a combination delete/backspace key. The entire keyboard is not shown, and therefore it can be assumed Alexis used a combination of keys to pretend to delete what was on the screen (i.e. command+delete)
About 5 minutes in, the first scene with Castle and Hayley walking down the street in Koreatown, Los Angeles. There are three signs behind them written in Korean lettering. The top sign is upside down.