Wilfred seems to have some of the same oddness that his granddaughter Donna has. The day before the end of the Earth everyone has bad dreams, but they can't remember them the next day. Except for Wilfred. He remembers his dreams including some about The Master who hasn't yet arrived. He also seems to share with his granddaughter a facility for finding the Doctor. The Doctor can literally be anyplace in the Universe at any time in history and he finds him in two hours. Finally, when The Master changes everyone on Earth into carbon copies of himself, the two people who aren't affected (other than the Doctor, of course) are Donna and Wilfred. After the Tenth Doctor's tour of duty ends everyone has gone through major changes: the Doctor, the Gallifreyans, The Master, and everyone on Earth...except Wilfred Mott. He's like a rock in a stream, the universe goes around him and doesn't touch him. He'll go back to his backyard astronomy and being endlessly nagged by his daughter just as he always was.
Wilfred Mott was played by Bernard Cribbins (born December 29, 1928, Oldham, Lancashire) He's an English character actor and musical comedian. He did a little dance step on his way to getting on a bus, not bad for someone 82 years old.