Plot hole: The Americans allegedly landed at Manchester on their way to kill the male Dragon in London. London is due south of Manchester. Why then did they head in the complete opposite direction to Northumberland?
Plot hole: Given that the dragons overwhelmed the worlds' militaries, the presented ways to bring them down are very gentle, so to speak. The force of impact on the ground would easily be achieved by an air to air or surface to air missile, or an RPG. The crossbow with some explosives has far less strength than a tank shell (weak points or no, the difference is just too great). The dragons are quite tough individually, but would have to succumb to strikes from modern weapons, or even to improvised ancient weapons of modern make. Humans that are able to keep helicopters and M1A2 tanks in running condition would be able to field several weapons that would bring down dragons quickly, effectively and nearly without their own casualties.
Suggested correction: There is nothing in the film to suggest that VanZan's men had access to any better weaponry that what they have currently. They have a tank but could be completely out of shells. They have vehicles and are maintaining them well, but that has nothing to do with whether or not they currently have access to any superior firepower. It is perfectly reasonable that any RPGs or rocket launchers would have been long depleted by the group before they began using crossbows and axes.
Plot hole: They make a big deal about attacking the dragons at twilight. But, apart from the poorly blue-screened shot of McConaughey on top of the tower, there's no sign that the final fight happens anywhere near twilight.
