When Henry first meets Clare in the library she tells him "You're younger than I've ever seen you." A virtually identical line is used in the Doctor Who episode "The Silence in the Library" when River Song meets the time traveling Doctor. Steven Moffat wrote both episodes.
Show creator Steven Moffat previously worked on the time travel TV show Doctor Who. That show also involved a red head who finds her life changed after she meets a time traveler when she's a child.
Henry tells young Clare that he can only go to times when he was alive. In the book, he says that he can go back as far as 50 years before and after.
When Claire shares her "Memorandum Book" with Henry, marking the 152 "dates" they have had, one of the days is "September 11, 2001."
Several times, a shot of young Clare's legs and shoes are shown along side a pile of clothing. This is the same image that appears on the cover of the book The Time Travelers Wife.