Claire tells Jamie she can't marry him because she doesn't know his real name. In The Garrison Commander (2014), Claire reads over the 'contract of marriage' where both her name and Jamie's full name is listed.
The previous day Claire receives a beating from Black Jack Randall, but the next day there are no bruises or signs of this assault.
When talking about his family Jamie tells Claire that his father is the younger half brother to the present master. Later it is revealed that he is the illegitimate son of the Master of Lovat and an older half brother to the heir.
Although Scotland banned wearing wedding rings on the left hand following the Protestant Reformation, by the date of Jamie and Claire's wedding the tradition of left hand ring wearing had returned.
Jamie would not know the word 'hangover' as it related to the after effects of alcohol consumption. This sense of the word dates to the 1890s and is of American origin. It is, however, possible he could infer the meaning by context.
When giving Claire his new wife his mother's pearl necklace, he calls them 'real Scotch pearls'. He should have said 'Scots pearls' as in 'Scots whiskey'.