Four and Twenty Blackbirds - S1-E4
Continuity mistake: When the milkman places the third bottle on Mr. Gascoigne's steps, they are placed in the sun. When the neighbour approaches, the whole road shows no particular sunlight. Which is fine, as a sudden change of that kind is ordinary. When the other neighbour pops by the corner and inquires, there's a close-up of the bottles, and again there's visible and directional light, pointed differently than the first instance. (00:08:45)
Four and Twenty Blackbirds - S1-E4
Continuity mistake: Hastings carries the picture of the two brothers from Dulce to Poirot holding it by the bottom, top, side, depending on the angle. (00:13:45)
Four and Twenty Blackbirds - S1-E4
Factual error: At the art gallery, Poirot and Hastings are looking at a painting identified as "Man Throwing a Stone at a Bird" by the surrealist Joan Miro. But the painting featured is completely different from the real one. (00:21:50)
Four and Twenty Blackbirds - S1-E4
Continuity mistake: As Poirot and Hastings watch the farce, the sword gets grabbed from the table by two hands, the left one doing the lifting by the handle. But the comedian in the following shot has it in his right hand. (00:32:04)
Four and Twenty Blackbirds - S1-E4
Factual error: Great accuracy went into the dates of this episode - Hastings is following the outcome of the so called "Verity's Match", the 2nd test of the 1934 Ashes series, Australia vs England. The events then should happen between the 22nd and the 25th of June, 1934, compatible with the murder happening on the 16th, and being discovered 3 days after. This however puts it a year before "Murder in the Mews", previous episode where Poirot's dentist was referenced, and that happened in 1935 as stated in the letter to the Chinese laundry.
Four and Twenty Blackbirds - S1-E4
Plot hole: In the denouement, Poirot says explicitly that the culprit sent the letter to the victim - but the letter in question, in this dramatization was stated earlier (in a change from Agatha Christie's original) to be an invitation to the art gallery, and the culprit is not the manager/art gallery owner! In the actual short story the letter was a personal message of entirely different nature, written and authored by the culprit.