Just before Cortez fights Princess for the second time, Jo-Beth is seen being lowered in a cage and her arms and legs are shackled. After defeating Princess, when Cortez gets off an elevator, Jo-Beth is seen standing there waiting for him. There would be no way for her to get out of the cage as not only was she locked in tight but also because she clearly didn't have a key to use to unlock her restraints.
In the level "Machine Wars", if Mordecai Jones and Angel Forge die before you get to the tank, they will still reappear after the tank scene.
At the end of the second level (Scotland The Brave) Cortez picks up a photograph of Crow and Khallos. In the next level (The Russian Connection) when the picture is being taken, Crow and Khallos have switched places.
In the first level (Time To Split) a bridge is blown up followed by the Time Splitters' mother ship. In the sixth level (The Hooded Man) the mother ship is blown up then the bridge.
In the mission "Breaking and Entering" if Cortez goes into the ladies' restroom and looks in the mirror, two stall doors are always seen as open.