At the start of the episode when Alex brings Kara doughnuts Kara gets a big square piece of paper towel and puts two doughnuts on it. When the camera changes angle as she sits down at the table she is holding a smaller rectangular piece of paper and only one doughnut. Then when she gets up again the paper is big again and she has two doughnuts.
When General Mathers spoke to the missile silo guard, the guard informed him that they were at DEFCON 5 (no danger of enemy attack). In that case, the nuclear missile in the silo would not be fueled and Indigo would not have been able to launch it.
If the key to Superman's Fortress of Solitude weighs 1 million tons, the ice that the key is sitting on would almost certainly collapse under the weight of an object with that kind of size/mass ratio.