Brianna tells William that "The best way to destroy an enemy is to make him a friend." Though quoted by others, this originates with Abraham Lincoln who said, "Do I not destroy my enemies when I make them my friends?"
Jamie telling Claire that he dreamed of her in her "proper" time is a reference to the first episode when Frank encounters a ghost on his way back from Reverend Wakefields house.
If Frank and Claire really did regularly take Brianna to Disneyland on vacation, this would have put them in pretty rarefied company. Studies done by Disney in the 60s showed that less than 5% of Disneyland visitors came from east of the Mississippi. The reason that Disney built Disney world was to better accommodate the approximately 75% of Americans who, at the time, lived in the Eastern United States. Orlando was much closer to Eastern population centers like Brianna's native Boston.
Fireflies produce a chemical reaction inside their bodies that allows them to light up. This type of light production is called bio-luminescence.
When Brianna and Roger and Jemmy and Amanda arrive back in the future, they have no modern clothes, no money and no health insurance to cover the cost of surgery for Amanda, which makes no sense. Claire left her money and property in Brianna's name prior to leaving and Roger probably had savings. Anything they brought from the past would probably be worth quite a bit. The immediate aftermath would've been interesting, though.