Saturn is the god of the harvest and visually impressive; it makes sense for the wormhole to be there thematically.
Saturn's orbit is where the Monolith was in 2001: A Space Odyssey as well (in the book only; in the movie, it was Jupiter).
Saturn's rings also mimic the shape of the accretion disk around Gargantua.
NASA sent the crew up using a rocket to conserve resources for the mission. This allowed them to start the journey with an almost-full fuel tank.
Viewers familiar with chemistry might sneer at Dr. Mann's explanation of his planet's surface, which is supposedly low enough that the chlorine in the atmosphere doesn't reach itnote Chlorine is so heavy that in most atmospheres, it should sink to the bottom rather than remain floating. It's a hint he's bullshitting.
Quite a few viewers have remarked on this movie's pronounced similarities to 2001: A Space Odyssey, to which it could be considered a Spiritual Successor. In 2001, the heroes were human astronauts, and the primary villain was HAL 9000, a chillingly amoral robot who would do absolutely anything to keep the mission going. In Interstellar, the robots are unfailingly loyal companions, and the primary villain is Dr. Mann, a chillingly amoral human astronaut who will do absolutely anything to make his mission end.
In the parentteacher conference, the principal and the teacher are dismissive of sending Tom Cooper to college, arguing that the world needs more good farmers, rather than engineers, and explicitly cite Cooper himself as an example of the kind of good farmer they're talking about. It's apparent that, despite disdaining the farming life, Cooper is quite good at it — however, what we also see is that Cooper has found many ways of using his engineering skills to help out around the farm; he's built combine harvesters that pretty much drive themselves, uses scavenged drone parts in barns, etc. It's hinted that it's actually these which give him the edge over other farmers in the area. In other words, what the principal and the teacher clearly don't realize is that Cooper is a good farmer because of his college education.
How could they land on the ocean planet and not notice the giant waves from space? Remember, the timescale on the planet was 7 years for every hour on the planet. Those waves would be barely moving when viewed from space, and by the time they were close enough to see them, they were concerned with landing.
It's subtle, but Romilly's change in behavior is noticeable after the crew returns to the Endurance. He is slightly more socially awkward, with a bit of a nervous tic to boot.
The school teaching that the Apollo missions were faked. At first glance, this just seems to be a way to get kids to care less about science. Then you realize: they needed to explain away the fall of the Soviet Union as something other than that country's people wanting more national autonomy and consumer goods, given the current state of world society (unified world government, subsistence economy). So, they claimed the Soviet Union was bankrupted by its Space Program.
In the Hans Zimmer soundtrack, the only time percussion plays is when there is a time crunch for some reason. The tempo is usually slow and deliberate, except when on Miller's Planet, the percussion plays at nearly twice the speed, since outside clocks would seem to run faster from an observer on the planet. This isn't the first time Zimmer has used music tempo to illustrate an altered state of time, either; the entire soundtrack for Inception is based around this concept.
Gargantua seems a little strange at first, being a giant black hole in a solar system and all, until you realize that in its center is the physical representation of every point in time of a single bedroom. With a nigh-infinite amount of mass in a small amount of space, you can imagine the power it must have.
Coop says his wife was the calm one, seconds before he chews his daughter's teachers out without raising his voice. Who do we know who's trained to remain calm and suppress their emotions? Oh, yeah, pilots.
TARS tells Cooper "see you on the other side" just before ejecting himself into Gargantua, which is basically a one-way trip as far as anyone knows. This at first sounds like a continuation of his pithy personality, but on subsequent viewings, knowing that Cooper will follow him into Gargantua, it's actually a clever bit of foreshadowing, too.
At the beginning of the movie, Murph is startled by Coop walking into her room. She says "I thought you were the ghost." Well played, Christopher Nolan. Well played.
TARS is rather savvy about the entire situation and even takes steps to prevent Dr. Mann from leaving with the ship. This makes sense seeing as he was formally a Military Robot, he's supposed to analyze a situation and come up with the best outcome for his fellow troops to ensure their survival.
His willingness to take precautions against Mann are quite interesting. He doesn't do anything that anyone would actually notice. After all, there would be no need for Mann to dock with the ship solo, so nobody would ever know about what he did, so long as everything went according to plan. His trust setting is set at a good balance: he doesn't make anyone think he's watching them for treachery, but he'll take precautions so long as nobody will know he's taking them.
The Stable Time Loop. When Cooper and TARS sacrificed themselves to get the Endurance away from the black hole, they saved the human race - Thanks to Cooper's sacrifice, Brand was able to set up the colony on Edmunds' planet using Plan B; frozen embryos, exowombs, etc. A couple of aeons later, future humans realize that Cooper was in a unique position to create Artificial Gravity and preserve pre-colony civilization, so they decide to help him. Humanity had no future until Cooper decided to sacrifice himself to save it, and in doing so, he himself was saved in turn. Kind of like The Apotheosis of Martin Padway.
The reason old Murph is so insistent that her father should not see her die? She's seen how Outliving One's Offspring affected her brother. Granted, Tom's son died in infancy and she herself was dying of old age, but it still counts.
Even with multiple ships like that seen in the finale en route to Saturn, it's hard to imagine that more than a few million people made it off Earth before the end. Or maybe they got everyone, and a few million humans were all that was left. Given that at one point a character finds the idea that there used to be 6 billion people on Earth unbelievable, this is definitely plausible.
Remember Tom's insistence on keeping his family on the farm, even in the face of massive dust storms and crop failures? There was almost certainly a significant number of people who refused to evacuate Earth for exactly those reasons, leading to a lot of self-selection against particular traits. Probably darker than Nolan intended it to be. It's only through Murph setting his corn on fire that he decides to leave... but what if some people didn't do that?
Donald comments on how much he wants a hot dog at the ballgame, saying that eating popcorn is a travesty. Remember that every other crop has failed due to the Blight and the farmers are struggling to grow enough to feed everyone. It seems unlikely that any livestock are still being raised for meat. Also notice the meal that Older Tom's family sits down to eat consists entirely of corn-related foods. This aspect is never addressed directly in the film, but subtle touches like that really let you know the extent of the Blight.
This only goes for certain definitions of "horror," but... The Endurance includes a number of human embryos in "artificial wombs" for re-creation of the human race. If they had actually had to fall back on that plan, imagine what Cooper, Amelia, Romilly, and Doyle's lives would've been, with like 50 babies each to be personally responsible for, and no hope for at least a decade of any help from said kids.