Plot hole: After the nuclear missile has overshot the ship and is determined to be heading for land, a map on a computer display gives an indication of the missile's trajectory relative to the Nathan James and western Europe. After the nuclear detonation, an external shot shows the blast is to the port side of the ship, giving the impression the ship is on a southern bearing off the west coast of France. At the time of detonation, the bridge crew shield their eyes while facing the front of the bridge, which would give the impression the ship is pointed right at the blast rather than off the port side. Later, Master Chief Jeter reports that the jet stream is pushing the radiation north-northeast, as if to indicate the ship is currently sitting in the fallout zone, when this would actually be pushing the radiation cloud away from the Nathan James.
Plot hole: The grounder's leader Anya states that the missiles (flares) burned a village to the ground. If this were true, the flares couldn't have flown very far, otherwise that village would have been too far away for the grounders to know about. In a previous episode, when you saw the flares from space, it was obvious the flares traveled hundreds if not thousands of miles away. (00:31:30)
Revenge of the Rogues - S1-E10
Plot hole: During the fight at sundown, Cold gets a hit on Flash and he goes down. Eddie takes a shield and goes to help. But Flash was in the middle of the street with no obstacles around, and it's implausible that Eddie could have gotten to him without Cold or Heat seeing him.
Plot hole: The nuclear explosion is on Liberty Island, a small yield, but nonetheless big enough to move an enormous amount of water towards the coasts on all sides. When we see Sertrakian and the others at the harbor no water is heading their way - they should be washed away by it. (00:37:30 - 00:38:45)
Plot hole: To identify the owner of a severed leg, Pride asks Loretta if she can guesstimate the body's general build by the foot's boot size. A much simpler way would be to swab for blood where the leg was severed and run it through the military DNA database.
Plot hole: They need at least 12 magnets to make it work, Paige collected 11. (00:21:00 - 00:22:00)