Poirot and Hastings arrive near Keswick on a train. This being the 1930s means the train should be composed of LMS loco and rolling stock. But the loco is a GWR 'Prairie' tank and would not bee seen in the Cumberland in the 1930s. Furthermore the carriages are British Railways stock dating back only to the 1950s.
Simpson tells Eliza Dunn she will need to go to Kings Cross station [in London] to start her journey to Keswick. This is incorrect. She would need to go to Euston station to get to Keswick.
Hastings and Poirot are depicted at Carlisle station returning to London but carriages visible seem to be GWR stock. Not something seen in Cumberland in the 1930s.