In the caravan setting out from the village when the situation on Earth hits bottom there's a clear outline of a Mercedes 190 radiator, showing the Mercedes emblem. That point in time is two generations from now, making that car, which was manufactured up until early 2000, roughly 74 years old.
When Getty is at the house with Murph to check on Coop's lungs, he notices Lois coughing. When he asks her how long she's had her cough, she replies off-camera "A while." However, her reflection can be seen in the window behind Getty, & as she says "A while", her reflection instead shows her coughing into her arm.
While docking with the Endurance, Cooper calls out distances in feet. NASA uses the metric system, so he should have been calling the distances in meters. Of course, since it was a while since he worked for NASA, such mistakes were bound to happen.
During the docking crisis scene, CASE analyzes the Endurance's spin at 67-68 RPM, meaning the entire station should complete a little more than 1 rotations per second. However, the actual RPM observed by the viewers is significantly slower, closer to 20 RPM (or 1 rotation every 3 seconds).
Mann states that the air on his planet contains too much ammonia to be breathable, but that at the surface, "the chlorine dissipates", giving way to breathable air.
Ammonia is comprised of one nitrogen atom and three hydrogen atoms, with no chlorine in is molecular structure. Mann, being a scientist, would have known this.
Considering how important the Lazarus and Endurance missions were to the future humans, it seems highly unlikely that they didn't realize the importance of TARS when it was found together with Cooper (Matthew McConaughey) near Saturn almost 80 years later. They would want to download the wealth of recorded data TARS would contain about the Endurance mission, not just dump it in Cooper's museum house.
When Cooper sees the second wave approaching and orders the others back to the spacecraft, he says "we're in the middle of a swell".. Actually the region between two wave crests is a "trough", not a "swell".. (Although the extreme urgency of the situation could have understandably contributed to his error.)
Immediately, after the death of Professor Brand, When Murphy is transmitting the message to Dr. Brand, she says, "I am very sorry for your loss."
However, when Dr. Brand receives the message at the ship, it plays as, "I am sorry for your loss."
When Cooper is sitting in Murph's room following the sandstorm and contemplating gravity as the cause of the lines of sand on the floor, he tosses a coin onto the floor and it lands at the end of a line of sand and very near a joint where two floor boards butt against each other. Then in the next scene the coin has moved to much further up the line of sand and away from the butt joint of the two floor boards, even moving over at least one floor board width.
Once landed on Millers planet, and in the 7 Earth years per their hour time dilation field, the audience can see the receding wave that has just passed.
The event flow is real time and only takes a few minutes.
The next wave is almost on top of them when it's noticed and, considering the speed at which it arrived, there was too much action from that point before it actually hit, when they should have only had seconds.
Also, the crew didn't seem to panic enough for self preservation, since Doyle had died after lingering unnecessarily.
As soon as the ship is on the other side of the wave we see the next wave approaching in the background as the landing struts extend.
The action / conversation flow is continuous between the waves and is again only a few minutes, yet the dialogue leads us to believe 3/4 of an hour has passed while waiting for the engines to drain.
In terms of the context of the situation only around 10-12 minutes was experienced on Millers planet, meaning just over a year of Earth time which would have been similar to original expectations, yet 23 years passed for Romilly on the mother ship.
When Cooper sits on the bed with Murph,trying to say, "Goodbye," before he leaves, her necklace alternates from being on the outside of her t-shirt and the inside, as the camera perspective changes back and forth.
When the spinning spacecraft Endurance crew looks out their window at a small Earth as they pull further away, just before they all go to hibernation in their liquid-filled tubes, the Earth is spinning counterclockwise. However, in previous scene the Endurance was seen pulling away from Earth rotating clockwise as viewed from Earth.
The latter scene's Earth spin should be clockwise instead of counterclockwise.
Prior to Coops leaving Earth there are several scenes where he has a spiral bound notepad in his shirt pocket. Throughout these scenes the notepad spiral binding has a number of loops loose from the pad, then switches to an undamaged notepad and back again.
During the first dust storm, Cooper pulls the truck straight up to the house. As the family exits the truck and enters the house, the wind and dust is blowing from left to right of the screen. When Cooper and Murph exit the house after the storm, the dust is piled up on the wrong side (right side) of the truck.
When driving in the Truck before the tire blew up, Murph has a pencil in her hair. Moments after the blowout, the brother comments on the event by saying "Murphy's Law", Murph answers angrily while not having a pencil in her hair.
Cooper and Mann's shoes keep changing color from white to orange and vice-versa during their fight scene even though the scenes are believed to be continuous from the sequence. Both of them are seen to have orange spikes in their fight scene and both have completely white shoes later on in the movie.
At 1 AU from Gargantua, Miller's planet would be traveling at roughly 0.99c. In the companion book, Kip Thrope explains that Cooper made use of Intermediate Black Holes (IMBH) of roughly 10,000 solar masses in order to match this velocity. However, using a top speed of 0.3 AU / month (the rate that Endurance traveled to Saturn), it would have taken at least three months in Cooper's time (proper time) for the ranger to travel from an IMBH that was just 1 AU away from Miller's planet to Miller's planet. Given the time dilation in the neighborhood of Miller's planet, roughly 15,000 years in Earth time is needed for this leg of the trip. Another three months from Miller's planet back to another IMBH gives a best case scenario of 30,000 years (Earth time) for a trip to Miller's planet and back.
The rocket launching from the underground facility was portrayed as a three-stage Saturn V booster. The rings of office windows would have been blown out on launch. Saturn V test firings in Alabama were known to routinely blow out windows miles away.
Harvesting machines appear in one scene, suggesting harvest is underway. Corn is not harvested when it is green. The plant has matured and the ears ready for harvest when the stalks and leaves appear dried-out, light brown in color or "dead" in appearance. Also: drought or "dust bowl" conditions would not produce the high stalks and robust rows of thickly-foliaged plants as portrayed in the film. The plants would appear sickly and short.
Approaching the black hole the gravity increases rapidly with the reduced distance to the event horizon (divided with the square of the distance between the two mass objects) i.e. if the distance is halved, the gravity increases by a factor of four. Getting really close to the event horizon every object experiences stronger pull to its parts closer to the event horizon than to those that are further away from it. All objects with mass and size (e.g. humans or space ships) would get torn apart as a result of different gravity acting on their parts. No one and nothing with mass and size can enter or even approach the black hole undamaged.
After Cooper decides he is leaving for the mission, during ascent in the Ranger TARS announces first that he is "beginning roll pro-grade" then goes on to say "prepare for stage 1 separation... Stage 1... there it is, Mach 1." Instead TARS should have announced reaching Mach 1 long before Stage 1 separation. At this point in the ascent by the time the first stage is depleted they would already be going much faster than Mach 1, around 2,300 m/s which is closer to Mach 7. This is possible because as the vehicle gains altitude, air density drops, reducing aerodynamic drag and increasing terminal velocity, allowing the vehicle to go much faster than possible at sea level. The Apollo program utilized its first two stages this way: the first main ascent stage (S-IC) was capable of reaching the edge of the upper atmosphere, but at this point the vehicle would still reenter as it does not have the necessary horizontal velocity to achieve a full orbit. The second stage (S-II) would then be activated to build the horizontal velocity needed to achieve LEO (Low Earth Orbit). Staging is done this way on purpose (using maths) and is very important to save fuel, possibly the most important resource in space besides life support itself. In the movie, the rocket they show used to launch the Ranger is very reminiscent of the first two stages of the Saturn V (Apollo vehicle) with a Ranger attached on top. No operational launch vehicle has ever surpassed the Saturn V in height, weight, total impulse, or payload capability. As this is NASA and not a private space firm doing these missions, it is safe to assume they would re-use effective & proven older designs with slight modifications (payload is now a Ranger) to perform these missions, especially to save on time and development costs. Saturn V and Apollo program details per Wikipedia, knowledge of it per KSP and FAR.
When leaving Earth, a three stage rocket is used to launch the Ranger and four people (and a robot). When leaving the water planet (with 1.3 times Earth's gravity) the thrust from Ranger is sufficient to lift 2 people (and a robot). The combined weight of the other two people would not be enough to combat the additional gravity.
During the emergency attempt to dock with the spinning Endurance, CASE informs Cooper that the Endurance is hitting the stratosphere of the planet below, with Brand adding that the Endurance has no heat shield. Since the atmosphere is apparently dense enough to support "frozen clouds" (sic), the Endurance would have long burned up before ever coming close to the stratosphere.
The title of the film is technically inaccurate. Interstellar travel is between stars within a galaxy. According to Professor Brand the 3 potential planets (designated Miller, Edmunds and Mann) are in another galaxy. This required both Cooper's Endurance mission and the previous Lazarus mission to travel from our galaxy to another - which would be defined as intergalactic travel.
The "Population Bomb" with 500 embryos as described by Dr. Brand would never work with the level of resources and equipment sent with the Endurance. The 500 embryos would have to be put in 500 incubators for viable babies to be born, but there is no sign of that in the base camp set up by Dr. Brand on Edmund's planet. Not even enough food to feed the babies for the first couple of months either before they can crawl and scavenge for themselves.
As the shuttle heads into Miller's atmosphere and begins to vibrate, the reflections on the astronauts' helmet visors remain perfectly stationary. In fact, they would be vibrating and those images would be jumping as well.
The Dodge Ram truck driven by Cooper has a 6 speed manual transmission. As young Murphy is shifting and grinding the gears being called out loud, she is told second then third, neither of which are in the position she shifts into.
At 0:18:20 when they're leaving the car and rushing straight to the entrance door because of the dust storm suddenly there is another person helping them enter the building.
But he didn't follow them inside he just walks away to the left side of the house.
At 2h 9mins, during the spinning docking sequence, the G force appears to be forcing the two pilots to lean in different directions, instead of in the same direction. This is correct, as the spacecraft is spinning about its central axis and centrepetal force will act on the pilots in this way.
According to the exterior views of the Endurance, the individual modules would have very high ceilings. To move between them you would have to climb a ladder and then crawl through a tunnel and climb back down a ladder.
This is not reflected in any of the scenes we see inside the Endurance.
In "The Science of Interstellar" special feature, at 21min 03sec the camera flies over the outer rim of a galaxy. There is a whole collection of stars that fly with the camera, rather then past it. They appear stationary in the frame.
When Cooper and Murphy arrive in the truck at NASA, Cooper wakes her up and tells her it's the end of the road. Murphy sleepily asks him if him if he brought the wire cutter and goes back to sleep. As soon as Cooper steps out of the truck, she sits up wide-eyed and sits in the driver's seat. That was unusual and appears to be a conflict in acting directing.
When he meets the people of NASA, Cooper says the nearest star is 1,000 light years away. While the nearest star, in the Alpha Centauri system, is about 4.4 light years away, Cooper meant that it would take a ship 1,000 years to get there using the technology known at the time.
Current satellite technology can not only measure things like waves and topography, but it can do it in very fine detail. Surely the Endurance would have had similar (if not more advanced) technology on board. As such, surely they would have noticed the massive, fast moving waves on Miller's planet long before they started the landing process.
When Dr. Mann attempts to open the airlock of the Ranger he is on while attempting to enter into the Endurance, there would be basic mechanical, electrical and electronic interlocks preventing him from opening the outer hatch of the airlock while there is still atmosphere in the airlock and there is an imperfect mating of the docking mechanisms. This basic component of airlocks became standard in the 20th century.
NASA would need the help of significant industrial technology in order to build the Endeavor and the other spacecraft needed for the Lazarus missions. All indications are most of Earth's industry, especially its high tech industry, is no longer operating by 2074 as shown by everyone driving vehicles that are at least 60 years old and the old drone that Cooper and his family caused to crash near their home.
When Cooper has to reset all the automatic farm machines' GPS systems, this indicates that some agency, normally NASA, has been maintaining and replacing the GPS satellites as needed at a time when NASA is supposedly shut down and no longer existing. We know that NASA still exists, but is keeping its existence secret, so theoretically, it shouldn't be launching GPS satellites every so often. Indications are that most industry in the world has ground to a halt as well, shown by all the vehicles that are by this date, several decades old, so there wouldn't be much of a high tech industry available to build new GPS satellites.
Cooper and Donald sit on their porch before Cooper's departure, drinking what appears to be beer, despite the fact that all crops except for corn (including ostensibly hops and barley, ingredients in beer) are not able to be grown.
After Cooper wakes up at Cooper Station, the doctor tells him that Murphy will be arriving "in a few weeks." When Cooper goes to see Murphy after her arrival, the nurse tells him that Murphy was in cryo-sleep for "almost two years." This means that Cooper was in a coma after his rescue for almost two years also, yet he shows no external signs of a long coma, such as long hair, a full beard, long nails, etc.
When Cooper first gifts the watch to Murphy, it is around 8:20. When Murphy throws the watch on the floor, the scene was obviously flipped because now it shows it is 3:30, plus the direction of the clasp is reversed from normal watches.
The goof items below may give away important plot points.
After Dr. Mann blows up part of Endurance and sends it spinning, Cooper must match its spin by spinning the shuttle to dock with it. Both Cooper and Dr.Brand can be seen leaning toward the right when the shuttle starts to spin. They return to the upright position when the shuttle has successfully docked with Endurance and both stopped spinning by using the shuttle's retro-thrusters. When the shuttle and Endurance spin at the same speed, they are both in a uniform circular motion, so the only force felt by Cooper and Dr. Brand should be the centripetal force pointing towards the spinning axis, which is behind their seats. They should only feel tangential acceleration that can rotate their seats when the circular motion is not uniform (i.e. when the shuttle spins up and the shuttle plus Endurance slow down). The correct reaction should be: they lean to the right when the shuttle spins up, return to the upright position when the RPM matches, then lean to the left when they slow down, and finally return to the upright position when Endurance stops spinning.
After waking up on Cooper Station, Cooper walks by a memorial monument which lists the names of the Endurance and Lazarus astronauts. Each list is in alphabetical order, but in the Lazarus list Miller's name appears before Mann's.