One of the first scenes shows the team of Rahn on a small football ground. In the background you see two cooling towers, a big funnel with the word "SHELL" in white letters and a huge white-painted crude oil tank. Apparently, the film set was in Köln-Godorf with the refinery of "Shell Deutschland GmbH" in the background. Shell Refinery was put on stream in 1960 with one cooling tower (the second was build some years later). Tank No. 7 was build in 1965. In the early-50s, crude oil tanks with more than 100,000 m3 capacity and a diameter of nearly 100m were not technical standard in Germany.
When Matthias is at home and cannot follow the world cup, his brother comes in with a transistor radio. The transistor radio was only brought on the market in 1953 by Texas instruments and 1954 by Sony.
When Matthias and his father travel from Essen to Bern, they drive through some kind of mountainous area, apparently the Alps. But both, Essen and Bern, are located north of the Alps, so there shouldn't be any mountains...
When the world cup is awarded, we only see the German team standing in line on the pitch, with some reporters in the background. After the historical match, when the cup was awarded, the Hungarian team stood aside the German team along with the referees.
The closing credits state the team winning the trophy in Bern ("die Elf von Bern") never played together again. In fact, the Bern team played one last match together, which was a benefit game 15 years after the victory.