When Ivan and Carole have a brief talk on the banks of the Danube near the bridge, we see evening traffic on the quay at the opposite side of the river, with a considerable amount of cars passing by, headlights on. There would not have been this amount of traffic in Budapest in the 1950s.
When Adam Sors returns to Budapest after the 1936 Olympics, there is a brief shot of the train station in Budapest showing several Bzmot type trains that were first put in use in 1977.
When fencing for the gold medal, Adam Sors' opponent has his foot way across the line at the start. This would never be allowed at the Olympics.