Revealing mistake: When they leave the caravan park, look at the wheels of the caravan they are set up to rear steer like a truck trailer, rather than a normal caravan. When they exit the park the caravan tilts, giving a good view of the set up underneath.
Revealing mistake: At the end in Paris, the Eiffel Tower is lying on its side with its bottom arches intact showing no signs of damage, as if someone has just pushed it over.
Chosen answer: First it should be noted that this film is based on the Japanese novel "All You Need is Kill" by Hiroshi Sakurazaka, which is where the term "mimics" comes from and could be something lost in translation (they adapted to alien planet environments by mimicking the biology of the planet's life, not necessarily making themselves look like a certain species). However, in the film itself it, was said the aliens "mimic our every action", militarily speaking. This is of course because the aliens were resetting the timeline when an alpha died and knew what the military would do, but to the military (and news reporters) it looked like they were just copying our fighting style.
Bishop73