When Pete talks to Miranda for the first time after the murder, and is crouched with his back to the cell door, two plastic cups are on the floor. As he rises, the cups have changed positions. One is lying on the floor, facing Pete.
When Miranda flees from solitary after seeing Chloe and crashing into the two guards, she falls backwards with her head towards the solitary. In the next shot, she is lying the other way around, fighting.
At the end of the movie, they are supposed to be in New York City. However, as Chloe is getting into the cab, you can see a (partially burnt out) Tim Horton's sign in the background. Tim Horton's is a Canadian coffee shop not found in New York. However, in the years after this movie was made, Tim Horton's did open shops in New York.
When Pete is taking Mirandas blood pressure he holds the bell of the stethoscope against her arm with his thumb. This is incorrect for the same reason you don't use your thumb to check someone's pulse. The thumb actually contains a heartbeat too. If you use it to try to listen, as with the stethoscope when taking a blood pressure, or check someones pulse your likely to pick up the sound/beat of your own pulse. If you use your thumb to check your own blood pressure or pulse you will get an incorrect reading, because you'll be hearing/feeling your own heartbeat twice.