The Book of Poems
The book of poems Pierre offers Sergei is shown just a couple of times in the movie, but ironically it's quite important. It reveals a sort of distance between Pierre and Jessica, that Sergei could learn her favorite poem just from reading it. Funny, isn't? It was lying in the house, unread for ages, and if only Pierre had read it he would have discovered something new and intimate about his wife.
Also, Jessica has tendency of readers to write home addresses on books, which is how the KGB discover their apartment. Funny how people leave so much of themselves in the objects they own, and also how such a harmless thing can be turned against an innocent person in a dictatorship. It shows the fragility of life so well.
This world is a comedy to those that think, a tragedy to those that feel.