The characters from the TV series are reversed in this film version. In the original TV series, Kelly Robinson (not Alexander Scott) was the white guy and the athlete, while Alexander Scott was the black guy and the non-athlete. In both cases, however, the Bill Cosby /Eddie Murphy character was a less experienced spy than the Robert Culp /Owen Wilson character.
There is a scene where the agents are sneaking behind the bad guys using a tracking device. They start in the hotel and get into the bath house. In reality, the hotel and the bath are in the same building.
When Kelly and Alex are sitting in the BMW Convertible on the car-transporter they are driving to the north on the quay of the Pest side of the river, but when they drive off the car-transporter they are heading to the south at the Buda side. Note the "Freedom statue" on the right at the top of the hill (Gellérthegy) and the bridge (Erzsébet-híd) in front of him.
When Kelly and Alex leave the warehouse to go to the party at 20:00 they enter a Mercedes Benz S-Class Limousine (W140). However, as they approach the entrance to the party, when the scene is inside the car, the dashboard design is that of a Mercedes-Benz E-Class (W124). Also, the car that Alex and Kelly get out of is not a super-stretch Mercedes limousine with darkly tinted windows. It appears to be a standard stretch sedan likely a Mercedes-Benz E-Class (W124).