In the show, set in 1985, Jan Böhmermann makes a joke about the Diddlmaus, but this product character existed only in 1990, 5 years after the episode is set, and in 1991 it was sold for the first time. This is clearly intentional or improvised as after that Jan Köppen asks if it exists in the 80s and Böhmermann replied "I don't have a clue".
Jan Böhmermann announced the hashtag/connection code of the show in the style of the old BTX-device which is #asteriskhash*. However in the real BTX-devices the connection code always started with an asterisk, not with a hash sign (finished with a hash sign, however). But since Hashtags are traditions in the show these days and the code itself is called "asterisk hash" it is clearly meant as a joke and reference to the nowadays-hashtags.
Jan Böhmermann mentions the "new furniture house from Sweden" named "IKEA". However in 1985 IKEA wasn't new, as the first German IKEA branch was opened in 1974, so in 1985, when the show is set, it wouldn't be new. In 1987 there were 18 shops in whole FRG.
Jan Böhmermann references the RTL show "Tutti Frutti" a few times. The episode is set in 1985, 5 years before the first episode of "Tutti Frutti"