The train is announced as arriving at King's Cross yet the locomotive hauling it is a class 82 (or 83 or 84). Those locos ran on the West Coast main line out of Euston, drawing power from overhead cables. It could not have gone to King's Cross as it would have had no power source.
When Emma opens the door of the coach, the door stays half open despite the fact the train is moving at full speed.
Passengers are able to enter the baggage car freely. This would not be allowed on a real train, for they could steal luggage.
As Emma reads the paper on the train, you can see that the reverse side of the front page is blank.
Mrs. Peel immediately identifies the body on the floor of Steed's apartment without seeing the man's face.