The Disappearance of Mr. Davenheim - S2-E5
Factual error: At Poirot's, Hastings browses a copy of Speed magazine - but it's the August 1936 issue. The story is set in mid-October 1935 (not just for consistency with the rest of the season, but also because the newspaper brought by Hastings towards the end mentions Duff Cooper as Financial Secretary for the treasury, which is a position held in that year before the elections - which are also mentioned). (00:18:30 - 00:43:40)
The Disappearance of Mr. Davenheim - S2-E5
Factual error: Poirot reads a fake copy of the Daily Express with a big article about the mystery disappearance. What makes it a not so believable fake, besides the odd artwork instead of a picture (a clash of style with the real Express first pages), is that you can make out of the words of the article closest to the camera, and like it happens to other props used this season, it mentions the Abyssinian crisis...but saying that "Mr. Churchill himself made the only speech." Churchill was not in office in the 30s. (00:17:05)
The Disappearance of Mr. Davenheim - S2-E5
Factual error: It is shown explicitly that The Disappearance of Mr. Davenheim includes the fact that before going to his study at 4:30 PM, he starts the record player, with Tchaikovsky's "1812 Overture", and that the record stops at 4:45 PM. The problem with it is that Mrs. Davenheim during the whole 15 minutes stayed in the same spot, absent-minded, and in 1935 a recording of that song would have been on a three sided 72 rpm record, since 33 rpm LPs were introduced in 1948. (00:03:15)