Audio problem: Tom's wife coughs into her sleeve as the shot changes; when it switches to Murph's boyfriend, you can see her reflection in the window and she is not coughing. "How long have you had that cough?" he asks, and although she replies "A while," you can see in the reflection that she was originally filmed coughing again as a reply. (01:49:20)
Continuity mistake: When Cooper is trying to console Murph before he leaves, he explains that time will slow down for him. In the first shot of the wrist watches side by side, the watches read at slightly after 9:00. Then Cooper says when he returns they can compare and the watches are shown again. This time they read around 8:20.
Other mistake: In the docking scene, CASE analyzes the Endurance's spin rate to be 68 revolutions per minute. When the Endurance is shown onscreen, it is not spinning that fast - it is spinning at maybe 20 RPM.
Continuity mistake: At the beginning of the movie when Cooper and the kids arrive to the lake after they took the control of the drone, Murph steps out of the truck and leaves the door open, but in the next shot the door is closed and it's sure that in the entire scene there's no sound of a car door getting closed.