Father Ted/WMG

Dougal is the secret son of a priest.
It seems the only explanation for how someone so utterly unqualified could have become a priest: his mother threatened to go to the papers, and to avoid a scandal young Dougal was fast tracked through the seminary.

I'm about 50/50 on the chances that Bishop Brennan is Dougal's real father.
 * Do the words "You address me by my proper title, you little bollocks!" ring any bells?
 * No such luck - the proper title for a bishop in Ireland is "Your Grace".
 * I dunno, he did state in Grant Unto Him Eternal Rest that both his parents were dead. Of course, this is Dougal we're talking about.
 * Or maybe his mother kept the truth from him and claimed that his father was dead.
 * Or maybe Ted is his real father, he does act like a father to him, lampshaded in The Old Grey Whistle Theft. And Ted's real father is Jack!
 * And Mrs Doyle could be Dougal's mother. She certainly treats him like a child (she even bathes him), and Ted seems very jealous when Pat Mustard steals Mrs Doyle's heart... One big happy family.

Dougal is a lot smarter than he seems.
That diabolical laugh with the trophy in the Christmas Special? Completely genuine. He's an evil mastermind who plays Ted expertly through Obfuscating Stupidity. Being sent to the island is all part of his Evil Plan to take over the world.

Dougal is The Straight Man in a Cloudcuckoolander world.
Following on from above. The whole ‘Why not knock loudly?’ thing in ‘Cigarettes, Alcohol & Rollerblading’ seems to suggest this.

Father Jack is a former Soldier of Heaven...
...and the series is set in the In Nomine universe, probably a Bright Low Contrast game. He lost an Ethereal Force in celestial combat and became the madman we know today, but retained a massive amount of Corporeal Forces. His stranger shifts may be the product of willing Kyriotate possession.

The show is a crossover with Ashes to Ashes
Only it's in the priest version of purgatory instead of the coppers version.
 * Wait, so if you fiddle your expenses in heaven (i.e. the Dublin parish) you get sent back to purgatory? Our (English) MPs are fucked!
 * What if Ted, Dougal and Jack were never priests while they were alive and having to live like priests is their punishment in Hell.

Father Ted takes place in the same universe as The Snapper.
In the Irish TV film The Snapper (1993), actor Pat Laffan plays George Burgess, a lecherous middle-aged man who gets a young woman pregnant. In the Father Ted episode 'Speed 3' (1998), Pat Laffan plays Craggy Island's new milkman, Pat Mustard – a lecherous middle-aged man who gets numerous women pregnant.

Could it be that the two characters are one and the same? By the end of The Snapper, George Burgess has left his wife and is presumably homeless. Perhaps he fled Dublin and changed his name in order to escape the scandal that he had knocked up a girl, and so that he could continue his womanising lifestyle, and eventually ended up on Craggy Island? After all, 'Pat Mustard' does sound a bit like a pseudonym. The two characters have similarly selfish, obnoxious, horny personalities, although Pat Mustard is slightly more cartoonish and exaggerated, in keeping with the style of Father Ted. Considering the similarities, it's hard to believe it's all coincidence; the writers probably cast Pat Laffan because they had already seen him play this sort of role, and knew he could play it again. The actor aged between The Snapper and Father Ted, which fits with the idea that several years have passed between the two. And, as an additional link, Irish actress Rynagh O'Grady plays a minor character named Mrs O'Leary in The Snapper – she is best known, of course, for playing the recurring character of Mary O'Leary in none other than Father Ted.

Incidentally, this theory would mean that the other films in Roddy Doyle's Barrytown Trilogy – The Commitments and The Van – also take place within the Father Ted universe.

The reason the priests seem to have a One Hour Work Week is because none of their parishioners want them anywhere near them.
Well, would you want Dougal's help with your problems?