Apparently there's something about salmon fishing that makes it more exciting or challenging or interesting than going after other kinds of fish. Maybe it's got something to do with their habit of swimming upstream in order to spawn, but I'd think that would make it less challenging (since fish would be traveling more slowly upstream than they would be if they were headed downstream). There must be some reason that a Sheikh who already has plenty of access to other kinds of fishing in his native Yemen would want to invest a great deal of time and money to try to introduce salmon, but that's something that will apparently remain a mystery.
Dr. Alfred Jones (played by Ewan McGregor) is a very straight-laced man, even by British terms. He has a very dry sense of humor, is in a passionless marriage with Mary (Rachael Stirling), and is a government ichthyologist by trade and fisherman by hobby. On the other hand, while Harriet Chetwode-Talbot (Emily Blunt) has an extremely British-sounding name, her personality is less subdued than you'd expect for someone with that name. She slept with her new boyfriend Robert (Tom Mison) on the first date, never seems to get discouraged, and works for an agency that represents the extremely wealthy Yemeni Sheikh Muhammed (Amr Waked).
Harriet and Alfred are brought together when she conveys the Sheikh's desire to bring salmon fishing to his native country, and Alfred immediately (and sensibly) rejects it as a completely ludicrous idea. However, others higher up in the British government hear of the idea and see it as a potential way to improve British-Arab relations, particularly as their participation with the US in the war in Afghanistan is not well received by all (including Harriet, since Robert's army unit was recently deployed there, taking him away from her). Alfred receives pressure from his superiors to try to make the idea a reality. The Sheikh's willingness to spend absurd amounts of money (including to double Alfred's salary, and to spare no expense in any other part of the endeavor) and Alfred's ability to work in close proximity with Harriet for the duration of the project helped soften the sting of being ordered to do this idiotic thing, but even under the best conditions, he didn't have much reason to believe it would actually work.
It seems that the film is based on a novel by Paul Torday, and as far as I can tell, it's purely fictional. But that's a little hard to believe because I can't imagine that anyone would come up with a story this lame when there are so many ways they could improve upon the plot. It doesn't make a lot of sense to place so much emphasis on salmon fishing when there's ready access to other kinds of fish and no explanation as to what makes salmon better. It doesn't seem realistic that Harriet would be so completely hung up on Robert when they've only known each other for three weeks and there's no telling how long he'll be gone, when they could've just as easily made their relationship last for months or years It's hard to see the Sheikh as a generous man who wants to help his fellow countrymen with this project when there's so much wasted money for so little benefit (and what benefit there is may only be enjoyed by a small number of individuals), and that's only on the off-chance that the idea actually works.
In addition to the lack of credibility, the film also suffers from a lack of depth. There are more serious issues in the movie than the Sheikh's fishing options, but they're either so obvious or so ridiculous that it's hard to care about them. It's not an outstanding romantic drama, and there are far better British political comedies like In The Loop, Four Lions, and The Guard. It's not so much that Salmon Fishing in the Yemen is a bad movie as it is simply not a good one.