At the end of the episode, Reacher enters the diner and inadvertently bumps into a man exiting, who excuses himself. That man is Lee Child, the author of the Jack Reacher novel series.
When Reacher speaks with his mum, Leslie Fray speaks in French without any accent, as she is a native French-speaking actress (born in Lyon, France).
Fray, who plays Jack and Joe Reacher's mum is about the same age as the actors portraying the adult characters.
Mrs Reacher calls Joe, Joseph. In the books, Joseph is not his name, his name is simply Joe.
In the books, it says Joe Reacher is one inch taller than Jack. In the show, the actor Christopher Russell, who plays adult Joe, is the same height as Alan Ritchson, who plays Jack Reacher. Both actors are 6' 2". Jack is supposedly 6'5", and Joe would be 6'6".