My Awful theory.
Perhaps Wilf is one of the Doctors regenerations.
Wilf never fired his gun, maybe a throwback to how the 10th doctor says he hates guns.
Perhaps this is also how the regeneration will take place.(In that one or both of them is shot and killed).
Timothy Dalton, mentioned the "knock four times" as being the beat of a time lords heart. Now if Wilf's heartbeat "knocks four times" it signifies him as a time lord.
If Wilf is the Doc's final regeneration, and Wilf remembers he's a timelord(through fob watch/Time Lords unmasking him), then he would have crossed his own timeline.
The doctor is never supposed to cross his own timeline, as otherwise terrible things will happen(The end of time itself).
So perhaps, as Doc 10 said on TEOTP1, he will completely die rather than regenerate, but in order for Matt Smith's Doc to come into play, Wilf regenerates

.
Crazy thoughts and wibbly-wobbly, timey-wimey comes itno play, and we're ready for series 5.
Although there is always the possibility, that Wilf is in fact The Master, exiled to past Earth by the Time Lords for his current actions.
It would explain the bad dreams. In "Utopia", Prof. Yana mentioned hearing a constant drumming/hearing words such as "regernation" and "time lord" for much of his life, not just after he recognized and saw his Fob Watch. < This could be construed as Yana's bad dreams.
It would also explain why Wilf is unaffected, as he cannot change into The Master, if he is The Master.
Its all too much to take,

, bring on the final episode.