Early on, Claire mentions:
"They say the definition of insanity is doing the same thing over and over and expecting a different result"
That saying would not have been used during the character's lifetime, as the earliest known version was in the Basic Text of Narcotics Anonymous, which was published in 1981.
At the dinner with Collum and Lord Lovet a young man says something and Jamie calls him cousin. However he was Jamie's half Uncle not cousin being the son of Jamies grandfather.