Somehow communication was exchanged between people of two different galaxies within a short time period only. It would have taken months or years for information to be exchanged. Taking in consideration for the amount of energy needed to communicate with videos, the distance to be traveled and not to forget a wormhole in between these places, Dr Brand was able to relay information.
People fighting on the lonely planet. Dr. Mann faked his result. One day he would have to tell others about the same. Why are you fighting people? What do you want to achieve killing the pilot of your spaceship? Grow up people.
Black Hole does not let light escape. The hero Cooper is able to brace the black hole without his arteries popping out and fall into the time dimension in one piece.
He sends a message "STAY" to Murph and then goes back in time to tell them coordinates of the secret place. Decide you want to change the history or not.
He is able to see the past in time dimension, why not present or future. Is he in deep sleep?
All quantum data is sent via Morse Code. Just image the number of dots and dashes. With all equations, numbers and words. Still Murph is able to decode that starting point of the code and code itself.
My favourite, Anne Hathway (Dr. Brand) is still young after so many years. And Murph Cooper somehow knows that only she would be alive and others are dead and she is waiting alone to be rescued. Others with her never had thought to rescue Dr. Brand and only Cooper can do it.