All the listening/recording props used in the film are actual Stasi equipment on loan from museums and collectors. The props master had himself spent two years in a Stasi prison and insisted upon absolute authenticity down to the machine used at the end of the film to steam-open up to 600 letters per hour.
The punchline of the joke that Grubitz tells in the cafeteria, about there being no difference between Honecker and a telephone, is a play on the words 'aufhängen' and 'neuwählen'. In terms of a telephone it means hang up and redial, respectively. In terms of politics it means hang somebody and elect someone new.
Director Donnersmarck spent a month translating the screenplay into French and sending it to Gabriel Yared to entice his participation as composer for the film. For the scene in which Dreyman plays the Sonata For A Good Man on piano, Donnersmarck asked Yared to write a composition that in two minutes would turn Lenin away from all the atrocities he later committed. This pivotal scene was the germinal idea around which the original screenplay was conceived and constructed.
Although it was very common for national flags and coats of arms of the former GDR to be placed almost anywhere in public places and institutions, not a single one was shown throughout the whole movie (except for one artistic representation of the CoA, with the hanging rope over it, on the cover of Der Spiegel magazine).
The German DVD of this film was recalled due to some statements director Florian Henckel von Donnersmarck made in his audio commentary about the alleged activities of politician Gregor Gysi and actress Jenny Gröllmann as unofficial agents (IM) for the "Stasi" (secret police of former East Germany). New and old revisions of the DVD can be distinguished by a marking on the back spine (old retail/rental: Z4/Z4R, new retail/rental: Z4A/Z4S).
The trivia items below may give away important plot points.
Ulrich Mühe, who plays Stasi-officer Wiesler, lived in East-Germany as a stage actor during the period depicted in the movie. Just like Dreyman at the end, Mühe once read his personal Stasi file, and found out that some of his fellow actors had been (involuntary) informants to spy on him. When asked how he prepared for his role as a Stasi officer, Mühe simply replied, "I remembered"
The letter-opener that informs Wiesler that the Berlin Wall is open near the end of the film is the same Stasi officer that tells the joke about Honecker in the cafeteria near the beginning of the film (Unterleutnant Axel Stiegler).