Dick's performance at the national selection has a full orchestra and chorus, which would violate a Eurovision rule that an act may have no more than 6 performers.
The way the Eurosong voting system works here is reversed. In the real contest, each country is called to give out their points for other contestants from 1 to 12 (9 and 11 are skipped), not to have their scores read out to them jury by jury.
No Eurovision jury has ever given 'nul points' to another country directly.
The real Eurovision Song Contest is closed to priests. This also excludes all other religious themes and names.
One of the other contestants at the Song for Ireland (which we never see) is a band called 'The Hairy Bowsies' with a song called "You Dirty English Bastards". The real Eurovision bans most political content.
During their song, Ted and Dougal say the horse is 'a pony no more'. Ponies are members of the horse species 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).
When Dougal plays his record, he puts the needle on and music plays, but it's clear the turntable is not moving.
Ted's chest hair is still dry when they are in the swimming pool.
At the end of the episode the Roman numerals that signify the production year say MXMXCVI, which means 2106; it's actually supposed to be MCMXCVI, meaning 1996.
Irish Eurovision song selections are public events that do not have formal dress codes.
The ending of the story has multiple misuses of language: the French say 'nul points' when it should be 'zero points'; the Germans say 'Irlande' when it should be 'Irland'; the Dutch say 'Irlande, nul punteen' when it should be 'Ierland, geen punteen'; and every other national jury, Spain excluded, speaks gibberish.
Ted comes to the assumption that Father Benny Cake's song was called 'Vienna'. The song is supposed to have been No. 1 in England. In real life, 'Vienna' was recorded by Ultravox, was written by Midge Ure, and only managed No. 2 in England.