When Lady Millicent is standing on the table in the museum, she is wearing light tan shoes. But moments later she is wearing black shoes after she hops down and starts to run.
When Poirot visits the Natural History museum, Dippy the Diplodocus is displayed in the central hall. This dinosaur wasn't put on display until 1979. In the 1930's there was a display of African elephants.
When Poirot is cycling along the street for the first time heading to Lavington's house, a modern car is clearly visible on one of the driveways.
When Poirot is cycling down the road there is a bright yellow alarm box clearly visible on one of the houses he passes.
At the end, Japp asks Poirot if he ever thought about going to sea, to which Poirot replies that he would not. In fact, Poirot has been to sea many times. In The Million Dollar Bond Robbery and Problem at Sea, Poirot travels on the ocean for an extended period.