Kicking Bishop Brennan up the Arse - S3-E6
Revealing mistake: In the bit where Bishop Brennan realises Ted did kick him up the arse, he runs up to Ted's house with his cape flying right out. The attachments holding up each side of the cape are visible.
Chirpy Burpy Cheap Sheep - S3-E2
Revealing mistake: When Fargo brings Chris the sheep to Ted's place, Jack crashes down the stairs drunk and breaks all the poles of the banister. It's obvious all the poles have been pre-cut.
Chosen answer: It's characteristic of someone putting on a fake Irish accent.