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: Claire sits on a blanket and empties a bag of stuff on it. Then it seems empty when she takes it from the ground to hand it over to Henry. The stuff would have sounded and the blanket is to light when she takes it from the ground to hand it over to Henry.
Continuity mistake: When Henry and eight-year-old Claire are in the meadow talking about the possibility of Claire's parents getting a divorce, watch Claire's left shirt sleeve (audience's right). There is a big white thing (possibly a piece of thread) that goes back and forth from on her sleeve to not there at all between shots.
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.
Continuity mistake: On their wedding night he returns to bed, the lamp is on the left and then on the right.
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.