Adolf Eichmann was not particularly well-known as a Nazi outside of Germany until his escape from capture after the war. Prior to Eichmann's capture and trial which brought focus to his responsibility in transporting victims to the camps, the man most associated with being "architect of the Final Solution" was Reinhard Heydrich, who was assassinated during the war.
Sir Ben Kingsley claimed that he kept a photo of Holocaust survivor Eli Wiesel in his pocket while he was on-set, as a reminder of his historical responsibility, and also as a reminder that he was intent on honoring Eichmann's victims rather than focusing on Eichmann. This is something Kingsley has done before, as he was carrying a picture of holocaust victim Anne Frank in his pocket while playing Itzhak Stern in La Liste de Schindler (1993). Kingsley added that after his previous research of Nazis for other films, he found no surprises researching Eichmann, and was not inclined to spend an inordinate amount of energy on the man's psychology.
Harel, the Mossad Director who oversaw the capture of Eichmann, wrote a book, "The House on Garibaldi Street," that describes in detail the operation.
Eichmann was responsible for organizing transport of Jews by rail to the concentration camps and those actions (among others) were part of the basis of the guilty verdict handed down by the Israeli court. This relationship is not explicitly stated in the movie. However, it is alluded to in the opening credits in which a hand (presumably Eichmann's) is shown pushing pins into a map of central Europe with the names of concentration camps and European cities on small flags. Those scenes are interspersed with shots showing train schedules. At the end of the opening credits, the camera pulls back to show the map fully with red lines indicating the railroad routes to the camps.
The razor Peter uses for shaving says Solingen on the side. Solingen is a town in Germany which is renowned for the manufacturing of fine swords, knives, scissors, and razors. It is also the town where Adolf Eichmann was born.