When the Doctor is trying to say, "Go ahead," to Cass in sign language what he is actually saying is, "You're beautiful," which accounts for her surprise.
One of the cue cards Clara prepared for The Doctor reads: "It was my fault, I should have known you didn't live in Aberdeen." The Fourth Doctor had dropped an earlier companion, Sarah Jane Smith, off in a hurry in The Hand of Fear: Part Four (1976). Toby Whithouse (the writer of this episode) had revealed in an earlier episode, School Reunion (2006), that she had been left in Aberdeen when she actually lived in Croydon.
One cue card reads: "I didn't mean to imply that I don't care".
Cass is the Second character to be played by a deaf actor in the history of the series, the first being Tim Barlow, who played Tyssan in "Destiny of the Daleks".
Another cue card says: "I completely understand why it was difficult not to get captured".