At least twice it is said that the temperature is sub-zero; yet the soldiers are playing basketball in tank tops, you cannot see anyone's breath, and a vehicle drives through a mud-puddle.
In the close-ups of the spiders' faces it is possible at least sometimes to see they have eight eyes--which is the correct number for most species of spider--but the shots from the spiders' points of view are shown as either binocular or monocular vision (with no obvious reason for the discontinuity). Even with genetic manipulation to increase their size, the type of vision is not something that would change.
In the sunglasses of Dash and the others you can see the camera-crew.
April states they did their research in Utah because the cold weather was a natural barrier to any potential spider escape, but surely the military could find someplace colder. High temperatures in the Utah mountains often exceed 50 degrees in the summer.
When on the bus one of the characters state that there's no cell phone reception in the mountains,
It then cuts to a shot of one the first on screen characters getting a phone call whilst on the mountains.
When Dr. Summers tells Dash that she signed a non-disclosure agreement to not reveal her work at the lab, he says, "...so when does the non-disclosure calvary show up?" He meant "cavalry".