When Ray catches up with Claire in Rome, her hair length changes; when Ray followed her, it was a short ponytail/bun but ends up on her shoulder when they meet.
During the opening-scene fight between the two CEOs in the airport it is supposedly raining (everybody carries umbrellas). However, Tully and Garsik do not get wet.
Near the end of the movie, Howard Tully and his people listen to a recording of Claire's and Ray's conversation. A few shots later, the speaker is seen from behind, and it's neither hooked up to audio nor to power.
In the beginning of the movie, the captioning says they are at the US Consulate in Dubai, but they are actually at the One & Only Ocean Club Resort on Paradise Island in the Bahamas. The consulate in Dubai is a skyscraper, not the villa we see.
When Ray impersonate a pediatric cardiologist and meets Barbara Bofferd, he tells her that his team is waiting for him in Ethiopia to open a clinic there. Then he explains that he needs to go to Brussels to catch a flight to Nairobi, which does't make sense since Nairobi is in Kenya.