This moment is the first time John Grey has seen Murtagh since he was in Ardsmuir prison 12 years prior.
It is historically accurate for the characters to bow to each other during introductions rather than shaking hands. Although handshakes were becoming acceptable in the northern colonies, in the south a bow was the standard greeting until after the Revolutionary War.
In the books, William falls into the privy with a snake. However, during production it was very difficult to practically fit a child in a privy, and the actual scene was unable to be shot.
The new wedding ring Jamie gives Claire appears to be in the style of the original wedding ring Jamie gave her in the first book Outlander. It was described as "a wide silver band, decorated in the Highland interlace style, a small and delicate Jacobean thistle bloom carved in the center of each link."
David Berry, who plays Lord John Grey, grew up in Australia and had to slightly adjust his accent to sound English.