When Poppy pours the hydrogen peroxide on Alistair's wound it does not foam up revealing that it is fake blood or the hydrogen peroxide is fake. Real blood has a component in it that causes the HP to foam up.
One of the simplest and easiest ways to determine if Alistair was telling the truth, which the main characters never think to do, would have been to ask him about local government and politics during his time. Such as who was the British Prime Minister, who represented Alistair's town in parliament, and who was the name of the local parish priest. It is doubtful a mentally ill man from the present would have known these things, and this would have confirmed Alistair's knowledge of the past to a much higher degree.
Great Britain actually still uses the Imperial system for measuring distance, so in both 1918 and now Alastair would have thought in miles. Nowadays the military does use the metric system for distance measurement to be standard across NATO.