When Michael is making the tapes, we see a notebook where he lists his recordings between 4 August 77 and 10 October 77. One of the entries is: Heinrich Böll, Women in a River Landscape. This novel was first published in 1985, so Michael couldn't have possibly read it in 1977. (Someone probably confused this title with another novel of Böll's, "Group Portrait With Lady", about the life of a woman born in 1922, which came out in 1970 and was very well received and popular at the time.)
In the street scene just before Michael and Hanna go on their bicycle trip (1958), a Volkswagen beetle drives by which has amber turn-signals in the taillights; these were not introduced until the 1962 model year.
When the movie starts in retro history and we see Michael go back to thank Hanna after his sickness and he sees her put on the pantyhose, it's labeled as 'Neustadt, West Germany, 1958.' Pantyhose weren't invented nor available on store shelves until 1959 - almost a year later.
During the cycling holiday, when arriving at the church, Hanna gets off her bike on the right hand side of the bike and walks towards the church. When she parks the bike against the wall in the next shot she is standing on the left of the bike.