In a scene where Leipzig is showed from the top the church "Probsteikirche" can be seen in the background, which was built between 2013-2015. The scene takes place in 1989.
The green West-German passport Anne is showing her dad was not in use since 1988. In 1989 it should have been purple. And the temporary passport that was used later in Germany after the reunion was also green but had a different cover layout.
When Egon Krenz asked since when Margot Honecker is commanding Erich Honecker around he gets the response "Since 1950". This is obviously a reference to their personal relationship. However Erich Honecker and Margot were officially married since 1953 and had an affair since 1948.
While being arrested Anne says that her father has no balls. The German version of this phrase (keine Eier in der Hose) was used in Germany in the beginning of the 21st century, not in the GDR of 1989.