INTERSTELLAR SPOILER BELOW
For example, how did he survive inside a black hole, how did he pass through the Schwarzschild radius with his simple spaceship, why was there no time dilation as he approached the black hole, why did his spaceship break down inside the black hole but he was able to eject with his simple spacesuit and survive, how did he realistically survive out in cold space (at the end, yes okay I know this is technically possible but still..)?
When I watched this movie, I saw a lot of problems that made me think "has a physicist ACTUALLY worked on this and said 'yes, this is accurate'?". And those certainly weren't the minor details like the time dilation on the planet, the structure of the black hole and the icy clouds on that one other planet.
Disclaimer: I enjoyed Interstellar a lot, it was a pretty good movie, although I felt that at times the director was pretty much screaming in my face: "SEE? WE ARE SO REALISTIC! LOOK THERE IS NO SOUND IN SPACE, AREN'T WE REALISTIC?" (sorry for caps lock but it's to provide emphasis)