At the beginning of the movie Jo has coffee spilled on the front of her top, the stain changes position and size from take to take.
Captain Kelly's bio states that he had been serving for 15 years, but unless he had multiple combat promotions (not really done anymore), it would not be possible to make Captain in 15 years.
A Navy SEAL would not have any online presence such as social media where a picture would be displayed. SEALS operate covertly and are at risk for retaliation from enemies of the U.S. If they could be identified from social media, then they would not be able to go on covert missions where anonymity is necessary.
In the photo, Bacic wears Lt Commander stripes, yet is identified as a captain in the caption.
Perhaps it's part of yoga but when Molly is telling Jo and Colin what to do, she herself is doing the exact opposite.
At the photo shoot for the book cover, when Jo steps in to make Colin feel more comfortable, she is on the right and Colin is on the left, from the vantage point of the photographer. Jo and Colin are positioned in such a way that his service rack (service ribbons) on jacket is not visible. So, there is no way that the image that ended up on the cover of the book could have been one that was taken at the photo shoot with Jo, since just flipping the image would not have produced made the rack more visible, not to mention the part in his hair would be on the wrong side.
The last scene of the movie is supposed to be in the bush (AKA Forest) in New Zealand. The flora in the scene is completely different to that of the New Zealand bush, no matter where you go around the country.
Jo says she has never traveled internationally. That means that she had never obtained a passport. Therefore, she would not have been able to fly off to New Zealand at the last minute as portrayed at the end of the movie.