Continuity mistake: When Henry goes to see Clare at the meadow and Clare is about 18 (after he gets the vasectomy) he kisses Clare, and each time they switch between Henry and Clare, the hair clips on Clare are a different color. The first are aqua blue and then they are yellow and back and forth for the duration of the scene. (01:03:35 - 01:04:40)
Continuity mistake: When Henry is telling Claire about his vasectomy, the paper mold on the table in front of her is right-side-up in one shot, then upside down, and then back to right-side-up.
Answer: He's really dead. But while he was alive, he time-traveled far into the future and saw Clare and Alba. His "individual timeline" is scattered, out of chronological order, all over the "real timeline, " so he can appear in the "future" as a younger (or, in this case, living) person.