Errors in geography
When Charles picks up Audrey right after she had a fight with Nick, they're all still in Monaco, but if you pause the movie right when the car pulls away, you will see that that scene was actually shot in Milan: You can see the classic "M" of Milan's metro and on the right is a road sign that says "Area Pedonale" in clear Italian.
When the Juan Carlos is being pursued by the Spitzes in their Ferrari Testarossa he shouts "faster" to his car when he sees them easily catching up to him. The Alfa Romeo Giulia Quatrofoglio Verde he is driving actually has more horsepower, faster 0-100 acceleration and a higher top speed than the Ferrari. So being a Formula 1 driver he should have no problem outrunning someone not used to driving a sports car which also happens to be the slower car.
There are three ranks of detective in NYPD. The first two levels are decisive by the police commisioner, Detective Grade 3 and Grade 2; Grade 1 is a civil service test. Further Nick is a sergeant; this out ranks a detective so it is unnecessary for him to take the detective test. All police officers are trained with investigations.
While on the yacht heading to Monaco, Juan Carlos Rivera is congratulated for "racing in the Monaco Grand Prix tomorrow." All drivers are required to be at Monaco no later than the Wednesday before a race on Sunday. There are two practice sessions on the Thursday and a short practice session followed by a qualifying race on the Saturday.