Earlier in the series it is determined that the alien airships are attracted to the heat output of roughly 500-600 humans in groups. So it is determined to break up the survivors into smaller groups of 300 (200 civilians & 100 fighters) in order to avoid this detection. Yet at the school that they eventually camp in as a base of operations in shortly later, they have LOTS of candles lining each hallway of the school for lighting. The problem is that a human body puts out approximately the equivalent of a 100 watt lightbulb in heat energy and a standard tealight candle puts out about 34 watts of energy. Therefore just THREE candles would equal the heat output of just one human which they are trying to avoid.
Anthony holds binoculars backwards. Two other guys look through them before they are passed to him and he doesn't know how to use them. This isn't just for a second. They show him two or three times and he continues to act without seeing anything because they are obviously turned the wrong way.