Approval of God: Andy Weir really has shown his work on the science involved in his book, especially in how NASA deals with situations arising from manned missions in outer space. And the people of NASA loved the book so much, they even adapted some of Watney's invented terminologies, like the "pirate-ninja" unit of measurement for power consumption per solar day, in their actual work.
The film adaptation was able to take into advantage NASA's fondness for the novel by having the agency review the scientific aspects of the story treatment pro bono plus permission to display the NASA logo in their spacesuit and spacecraft props (Note that NASA, as a public, tax-funded agency, does not take too lightly on attempts to "commercialize" their brand and the work they do). Needless to say, however, NASA also benefitted a lot from the film's popularity in bolstering public interest on the ongoing Mars exploration program (the Opportunity and Curiosity rovers), paving the way for a possible manned mission to Mars.
Creator Backlash: Two very minor examples from Andy Weir: He wished that the book opened up with Watney getting stranded instead of showing that event later, and that the story used a more realistic reason to leave Mars than a dust storm (which in real life would not pose a threat to the astronauts) though he admitted the dust storm felt like a necessary force for a man vs. nature story. The former issue was corrected in the film adaptation.
The Moral Substitute: By the author himself. As of October 2015, Weir is working on a Scholastic Edition of The Martian for purchase by school libraries, which involves substituting all the swear words.
Science Marches On: This book is an odd case, because it has an enthusiastic following within NASA, specifically the Jet Propulsion Laboratory, which runs Mars surface probes and orbiting satellites that are directly responsible for disproving some of the book's assumptions about Mars.
When Andy Weir was still writing, it was unknown how much water might be recoverable from the surface, likely very dry apart from the frozen poles. This is why Mark Watney burns hydrogen (catalytically cracked from leftover hydrazine)—to collect the water. Then Mars rover Curiosity finds that the Martian soil is loaded with ice particles—as much as 35 liters of liquid water per cubic meter of soil. The Martian had been published by then, but Weir didn't let it bother him. There are still dry areas, though, so burning hydrogen for water could still be necessary in certain situations.
It's now believed that liquid water flows on the surface of Mars to this day; some of the evidence coincidentally was discovered at Acidalia Planitia, where the novel is set. On the other hand, this water is without doubt extremely salty and acidic due to high percentage of chlorate salts in the Martian soil which lowers its freezing point enough to allow it to remain liquid, but makes its unsuitable for agriculture without distilling.
Ability over Appearance: Kapoor was Indian in the book but after Irrfan Khan was unable to come on board, he was played by Chiwetel Ejiofor. The character was then rewritten to be half-Indian and half-African, and his first name was changed from Venkat to Vincent. His religious background also changed, making him half-Hindu and half-Southern Baptist.
Approval of God: Andy Weir very much approved of the film version, even going so far as to say he almost cried in the first four minutes just to see his book come to life on screen.
Backed by the Pentagon: The production team heavily collaborated with NASA for the film to make absolutely sure they got everything right. It helps that the Ares missions depicted in the story are based on real NASA plans for a voyage to Mars in the 2030s.
Since mankind has yet to visit Mars, much less film there, a location on Earth had to be selected. In this case not California (or the American Southwest), but Wadi Rum, Jordan. This is a red-colored desert.
Budapest Doubling: The Chinese space center is a very recognizable building in Budapest (without the Chinese writing, obviously), with a similarly recognizable bridge in the background. The interior shots of NASA's mission control were also shot in Budapest in a shopping center / office building practically next door to the "Chinese space center".
Dyeing for Your Art: Averted. Matt Damon was willing to lose weight to show the effects malnutrition had on Mark Watney's body but Ridley Scott opted to use a body double instead.
Executive Meddling: Ridley Scott was against calling the meeting The council of Elrond because he felt it was too meta having cast Sean Bean, insisting he use some other nerd reference, however executives insisted it stay the same as the book.
Fan Nickname: Russian-speaking watchers immediately dubbed Mark himself and the movie in general The Belorusian, because of all the potatoes.note For those who don't get the joke — in Eastern Europe the Belorusians are stereotyped as potato eaters to an even larger extent than the Irish, to the point that the common nickname for a Belorussian is "Bulbash", from "bulba" — "potato".
Reality Subtext: One of the promo videos has Mark making a joke about the Cubs holding off on winning the World Series until he gets home. Martinez, offscreen, snarks that it'll be easy, but this was written back before the Cubs finally won in 2016.
Throw It In!: Donald Glover tripping and falling while he gets up for coffee was a genuine mistake on his part. Ridley Scott decided to leave it in.