When Renée's father is bleeding from the ears, Syd said his pulse was all over the place. There is no way she could have known this in such short time.
Look closely: When Tom blows up the van outside Renée's apartment, you can clearly see wires attached to lift it in the last shot.
When Rachel and Dixon are in the facility and when Dixon says, "Yeah. I've heard that before. " there is a boom mic behind him that can be clearly seen.
When Marshall shows Dixon and Rachel his tomographic camera, he asks if they have arachnophobia (fear of spiders), however he then goes on to explain that the device has six legs, which would classify it as an insect. Spiders have eight legs.
When Thomas Grace is at the firing range, he pulls the trigger over and over past the number of bullets he has, called, "Dry Firing" (which is harmful to the weapon). A highly-trained agent should not be so careless, and should be keeping count of the bullets he's fired, even while practicing.