Plot hole: In the course of the story it's said that at the time the black hole went out of control, it had a mass of "half a mountaintop of granite." But in a flashback scene Dr. Krone is shown growing the mass of the hole by feeding it large numbers of lead bricks in the laboratory. It's a little hard to believe his lab could store, or even afford, enough lead bricks to equal that much mass.
Revealing mistake: In the very first scene, which takes place in a Moroccan sheepherder's meadow, the camera makes some gentle panning motion. The mountains in the distance can be seen noticeably moving not quite in sync with the foreground. The foreground is actually in Texas (according to the director's commentary), and the mountains were added in post production.
Factual error: In the scene in which the scientists observe the emergence of the black hole out in the Lechuguilla desert, as it pokes out of the ground unexpectedly near to their base everything in the tent is shown powerfully accelerating roughly horizontally, toward the object as it whizzes skyward. But, given all the data in the movie(mass = 10^9 kg; it reaches max height of about 1,400 meters above the desert floor before coming back down; it emerges not less than 2 meters outside their tent), it ought to impart a gravitational acceleration of not more than 0.0167 m/s^2, which is only less than two thousandths the force provided by Earth. Given that the hole was also traveling away at about 117 m/s, the relative velocity would've been in excess of the hole's escape velocity(only about 0.25 m/s), so there would be no such dramatic effect.