At 05:30, we can hear the news anchor mentioning a fire in a chemical plant and subsequent problems on the waterways. He's referring to an actual event: The Sandoz chemical spill (in German known as the fire of Schweizerhalle). A fire destroyed a chemical plant on 01. Nov. 1986. Several toxic substances were flushed into the nearby Rhine river when the fire fighters tried to extinguish the fire. The aquatic life in the river was severely damaged for several years.
The cassette tape with the controversial song Katharina and her friends are talking about is most likely the song "Jeanny" by Falco. The song was boycotted by several radio stations but sold over 2.5 million copies to become the best selling single of 1986 in German-speaking countries.
Ulrich is playing on a Commodore 64, the most popular home computer in the 80s. The game he plays is "Commando".