Most shots of Entebbe Airport include a long line of African flags running alongside the terminal, between it and the runway. The line includes the flag of the rebel Republic of Rhodesia (now Zimbabwe), which neither Uganda, nor any other country, recognized.
When the children run beside Idi Amin's car and wave to Garrigan, thinking the president is inside the car, a digital wristwatch is visible on one child's arm, especially in slow motion at the end of the film.
When the President and the Doctor travel to Entebbe airport in the soft-top Mercedes, two white Bedford trucks block their front and rear. The trucks are AWD Bedfords with a silver AWD logo mounted on the front. AWD took over Bedford trucks in 1989, ten years after Amin was removed from Uganda.
Idi Amin held the rank of General until 1975, then promoted himself to Field Marshal. Throughout the movie, he wears insignia of both these ranks at differing times, making it appear that he continually switched between them. On the 'working' uniform, he always appears as a General (crossed swords, pip and coat of arms). In his 'dress' uniform he always appears as a Field Marshal (crossed sword and baton enclosed in oak leaves).
The goof item below may give away important plot points.
According to the closing sequences, only one hostage was killed during the rescue operation at Entebbe Airport. In real life, three hostages were killed during the raid: Jean-Jacques Maimoni, Pasko Cohen, and Ida Borochovitch. A fourth hostage, Dora Bloch, was killed by Ugandan army officers at the Mulago Hospital in Kampala.