In the opening scene, where Carter is directing traffic, at the second accident, the girl in the Mercedes hits an 80s era Monte Carlo, but when Carter is talking to her, he calls the other car an '81 cutlass.
When Carter and Lee have their first gun fight together, Carter runs out of bullets. When Lee slides across the floor to 'load' him, a bullet is already present and visible, ready to shoot. He never cocked the gun, or had time to, in order to load and shoot.
When Carter is sitting at the café (probably Café de la Paix) in front of the Opera House he sees the name Geneviève advertised on top of Théâtre des Champs-Elysées. The theater is on Avenue Montaigne in the 8th arrondissement, a little less than 2 miles away.
In the beginning of the movie, Carter (as a uniformed police officer) is seen directing traffic flow in Downtown Los Angeles just before the ensuing accidents he causes. In the City of Los Angeles, however, the police officers of the Los Angeles Police Department do not direct traffic. Instead, that job is assigned to traffic officers (noted by their brown-colored shirts, yellow safety vests, and white caps) of the Los Angeles Department of Transportation (LADOT), not the LAPD.
The Paris Commissioner announces himself as DGSE. The DGSE is France's military and counterespionage wing. It has nothing to do with internal security or police work. He should have said Police Nationale, which runs Paris law enforcement and, as a subordinate of the Ministry of the Interior, handles matters involving foreigners.
When Kenji targets Ambassador Han, he rotates his rifle after having Lee in his scope. At that range, the rotation degree would've clearly put the shot outside the building Ambassador Han and Lee were in.
The goof items below may give away important plot points.
When Carter (disguised as Genevieve) steps out of the lift in the Eiffel Tower and cocks his automatic pistol, the sound produced is a second late and is recognizable as sound of a revolver being cocked