The movie basically cuts physics completely out of the story (no principle of least action, no diffraction), which makes the continuing presence of Ian awkward since he doesn't have much to do. I thought this was disappointing but inevitable; general audiences don't want a 20 minute physics lesson at the theater.
Less understandable for me was that the film also eliminated any of the functional interaction for how Louise (or any linguist) would go about learning a previously unknown language by interacting with a native speaker. All of the guess-and-check, experimental structure that goes into this lingual interaction is gone from the film. The humans and aliens talk/grunt to each other, look confused, and then Louise just periodically declares out loud that she's figured things out. In the book, laymen can at least get a hint of how a linguist (and physicist!) thinks and solves problems, but the audience learns nothing like this in the film.
Finally, the film has unambiguous communication backwards in time, violating the known laws of physics. I've talked to people say they saw this in the original short story, but I think a careful reading shows that, though the narrator adopts a framing of fatalism/predestination, none of the real-world events described by the narrator actually require retro-causation. In the film (spoiler!), Louise literally use memories of the future to figure out what telephone number to dial.
Also, the standard Hollywood tropes weren't as bad as they could be, but still distracting. Does every film featuring the military need a painfully one-dimensional rude hawkish general who inexplicably wants to attack the enemy in every situation?