The long, empty shot of the crew drifting past Saturn. Even though they're all still alive at that point, there is still such a profound sense of isolation and insignificance—and they still have so far to go. There is just enough time on this shot to allow all this to sink in. Now that is filmmaking. Special mention should go to the segment where they impose ambient noise from a thunderstorm against the image of the ship flying by Saturn. Blending powerful sounds of nature with the majesty of the cosmos.
When the astronauts first go through the wormhole and soar through infinite space, the imagery, mixed with the score, is fantastic. Renowned theoretical physicist, Kip Thorne himself provided the most up-to-date mathematical models and equations to the VFX department. So that scene, at least as of 2014, really is our best guess as to what it would actually look like.
While on Miller's planet, Cooper sees a tsunami is coming their way and orders Brand and Doyle to return to the shuttle. Except Brand gets stuck under a piece of debris while trying to recover the data log, so Doyle orders CASE to go save her. Up until then, CASE seemed like a clumsy, slow and blocky robot, but it suddenly makes full use of its shape-changing features, displays amazing moving speeds through the water and saves Brand in a flash.
Murph torching Tom's crops to draw him out and save Tom's family from himself.
CASE casually reveals that TARS turned off the auto-docking to prevent Dr. Mann stealing the Endurance, due to the latter robot's low trust settings.
Cooper coupling the landing craft with the Endurance after Dr. Mann, in his mad attempt to hijack the ship, severely damaged it. It should be noted that he does this while the Endurance is spinning at 68rpm. And he doesn't black out, even though the g-forces of that spin did knock out Brand.
It was doing more then spinning. It was hard to see, but the Endurance was actually precessing, that is, spiraling around its new center of gravity like a Spirograph wheel. So CASE and Cooper didn't just have to match the spin but the spiraling motion. It was a monstrous feat and could not have been done without both working together perfectly.
CASE: It's not possible. Cooper: No. It's necessary.
TARS' part is to manually dock with Endurance, which Mann was unable to do even under calm conditions. Despite the spiraling, TARS is able to calculate by single degrees and perform the docking to perfection.
The 5th Dimension (no, not that one): Or at least how it's translated in 3-dimensional space as a hyper-cubic, grid-like tesseract composed of perpendicular, time-bending gravity waves (or something like that) inside the black hole created by the "Bulk Beings" who transcend 3-D perception of time and space. It is what enables Cooper to send the necessary data for Professor Brand's gravity equation to Murph to successfully crack the equation, and save humanity.
The way in which the tesseract displays every single moment of Murph as a young girl and as an adult walking around in her room as separate 3-dimensional constructs. It's just such mind-blowing, trippy imagery as only Nolan could do.
Cooper toggling a "wave bar(?)" to manipulate one of the hands on adult Murph's watch to tell her the gravity data in Morse code.
Cooper Station. Especially since not only is it a functional American space colony orbiting Saturn, implying that civilization's recovered beyond Earth, but that all it represents was made possible by both Cooper and his daughter. The fact that even the family farmhouse was moved to the colony is just icing of the cake.
Like many other aspects of the film, this location is based on the O'Neill cylinder, a potential design for long-distance space stations that could be built in the future to explore the galaxy, and it's seriously cool to see one realised in full motion.
. Any other director would have just had Matthew McConaughey on wires in front of a green screen and make the set digitally. Not Christopher Nolan. One of the most impressive visuals in a movie FILLED with impressive visuals, and they actually MADE it in real life.