Continuity: Between the time that John leaves the airport and arrives at the hotel after chasing the taxi, he has shaved.
Audio/visual unsynchronized: Sophia lights a cigarette with a disposable lighter in the car as they leave the airport, but the sound is of the lid of a Zippo being flipped open.
Continuity: When John finds Nadia tied up in the hotel room (after her boyfriend has found out that she is pregnant), he unties her hands, but not her feet (which were tied up), there is a short fight between them, and it is seen that her feet are not tied anymore.
Revealing mistakes: When John knocks out Alexei with the guitar it clearly misses by quite some distance and doesn't break.
Errors made by characters (possibly deliberate errors by the filmmakers): Alexei and Yuri speak Russian with French accents.