Plot hole: In the air vent, we see a rat. Wouldn't rats in the vents set off the alarms on a regular basis, because the lasers were on the upper side of the vent?
Plot hole: Accessing the secure room through the duct work would be virtually impossible (pardon the pun). First is this an air supply duct, return air supply duct or an exhaust duct? If it was an air supply or a return air supply duct there would be a squirrel cage fan moving the air. Not the propeller fan you see in the frame. If it was an exhaust air duct again no propeller fan. The size of whatever duct it is for that size of a room is questionable. The room was small yet the duct was large enough for a man to crawl through. The last reason why this would be impossible is where are all the screws that ducts are assembled with? They would definitely stick through the ducts and catch clothing, scratch hands, heads etc.
Plot hole: There is no reason whatsoever for Jim to have brought the bible from the hotel with him. Max says that Job never quotes scripture in his messages, so he has no reason to bring the bible. The only biblical reference is job 3:14, and that is simply a phrase to remember: having the bible with you will not help you remember it in any way.
Plot hole: There is absolutely no way Jim Phelps would have "died" when he got shot even if he was faking it. The first time we see his death he's pointing his gun right at the camera on his glasses which are on his head and not his chest. Later when we see the how he fakes his death he's not pointing the gun at himself anyway so he wouldn't be able to get the angle of the gunshot from his camera's point of view as we saw the first time.
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.