Continuity mistake: When Ethan is being lowered into the room with the NOC List, he has the digital temperature gauge. As Ethan is going down, the gage is right side up so you can read it normally. However, Ethan is upside down, and therefore so are the camera glasses he is wearing. Now when we see the computer screen that Ving Rhames is using, the gauge is right side up there, but it should actually be upside down.
Factual error: Luther asks for a laptop with an "AI RISC chip". This is nonsense - RISC stands for Reduced Instruction Set Computer and is a description of the number of registers used by the chip - nothing to do with AI, which is a broad range of analytical and non linear heuristic techniques to enable a computer to learn and make non-deterministic (ie. non programmed) decisions.
Plot hole: In the famous raid on the computer room raid, where Hunt is lowered from the ceiling, we see a close up of the screws to the vent being undone and caught in a holder so they don't fall on the floor. But the screws cannot be put back in their holes and done up once the vent is closed, and there is not enough time for Hunt to be pulled back up and the vent closed and screws replaced when the operator returns to the room, as Hunt was pulled back up with seconds to spare.