Minor Plot hole: In the subway scene, Payne and Annie address each other by their first names even tough they never had the information before. Oops.
Major Plot hole: Jack Traven (Reeves) is a maverick Police Officer like we know them. He doesn't like to wait and is ready to jump into the action and be loud if it means that he will save people. So when he reaches the dreadful bus that has a bomb on it that will activate when the bus reaches a speed of 50 miles per hour, Jack, our maverick cop, tries to scream at the driver and subsequently hop on another dude's car to scream at the driver again, but LOUDER, to tell him that he needs to stop the bus. He could simply have shot the tires with his gun. The movie is over.
Major Plot hole: Payne says to Jack that the second he knows they are trying to leave the bus or create a plan to do so, he will detonate the bomb, even if it means losing the money.
This statement goes in accordance with Payne's action in the first bomb threat where he activated the elevator bombs when he heard the police try to save the hostages. So, it is very strange to realize that Payne was watching the bus with his camera, saw Jack leave it and come back inside FROM THE FLOOR, and did nothing about it. He did not blow up the bus and he did not bother to even mention it afterwards on the phone.
Unaddressed Issue: Sure Payne is a psychopath. It is also clear that he is intelligent and able to create complex plans in order to get what he wants. But why put his gold watch on the bus bomb? What could he gain from giving away a hint about his identity? Obviously he rigged his house with explosives, but that doesn't change the fact that he made the whole police agencies of the country know that he is a criminal. No one knew it was him before, why put this great advantage in jeopardy just to kill some other cops that would not have tried to kill him in the first place if they didn't know who he was?