In "A Christmassy Ted," Ted can't remember Todd despite Todd claiming that the two are former schoolmates. Clever Foreshadowing, don't you think?
The reference to the horse in 'My Lovely Horse' being 'a pony no more'. At first glance, this looks like artistic license (which it likely is). Ponies are members of the horse species (Equus caballus) that never grow bigger than 147 cm (14.2 hands in horse measurements). Therefore, young horses are NOT called ponies; the correct term is 'foal'. However, the word 'pony' comes from the Old French word for 'foal', but the meaning does not apply today. Ted and Dougal are presumably unfamiliar with horses (Dougal more so), and therefore they are not alone in making the mistake (albeit mistaking foals for ponies instead of the other way round as people who make the mistake usually do).
Why don't John and Mary get a divorce? Well Ireland only passed a constitutional amendment allowing divorce in 1996 and the Catholic Church still does not permit it.
Plus, under the law, a couple has to be separated for a number of years before they can officially divorce. Neither of them can probably afford to divorce.
Word of God says that John and Mary were supposed to be a dig at Ireland's divorce laws.
In the episode "The Passion of St. Tibulus", we are introduced to Mrs. Sheridan (already seen as a fortune teller) and Mrs. Glynn. However, when Ann Rowan who plays Mrs. Glynn returns, she is credited as Mrs. Sheridan. The fact that it's hinted they've shared a lover (Mrs. Glynn's husband Billy) suggests wife-swapping is going on.
In the first episode of the third series, Ted is shown in a nice, fancy parish in Dublin (at least until he gets himself kicked out after once again fiddling with expenses). His actions in the second series finale Flight Into Terror saved the lives of numerous other priests and nuns so this may have been his reward from the Catholic Church.
"Chirpy Burpy Cheap Sheep": Of course a priest would have an "intuitive understanding of sheep."
The only given reason why Ted, Dougal and Jack are on the island together is because of past failures. However, the offences for which they have ended up where they are implies deliberately exaggeration of the circumstances by Bishop Brennan.
The title of the second last episode is "Night of the Nearly Dead". Dermot Morgan died after the recording of the series.
Also Harsher in Hindsight is the first episode when Ted goes to a fortune teller at the fair and gets three death cards in his tarot. Dermot Morgan died after three series of the show.