Kate outruns the train while jumping aboard, but a moment later when we're watching the wheels pass in front of Max, it's moving at about 20 mph.
In the freight train, Kate's shirt changes repeatedly from a relatively clean white shirt to a dirty gray-stained one.
Kazak tries to finish the bank transfer, even though the bomb which has already exploded, some ten feet away from the computer as established in previous shots, is causing the ship to blow up one section at a time.
When Max jumps on the train it is daylight and just moments later when he is kissing Kate it is dark.
After detecting the cellphone, one of the villains says "I have triangulated their position," but rather than a position, his display indicates a route of travel several miles long. Either the display is wrong or it is indicating where the phone has been for the past several minutes; in the latter case, the position could have been given that many minutes earlier.
If there were such a thing as a heat sensor, it would also detect hot water pipes when they had recently been used; and someone taking a cold shower would not seem to vanish, because the warm core of their body would still be detectable behind the cooled skin.
Electronic door locks in hotels do not have the capability of locking people into the rooms, whether by central control or otherwise.
Kate drives a manual transmission car without using the clutch.
In an otherwise correct list of international currency codes, the bank computer displays the Japanese Yen as YEN instead of JPY.
The interface depicted for the funds transfer is a bizarre and nonsensical combination of a computer display with an audio-based system such as would be used for access by simple telephone.
On the train car, when Kate sits up quickly and points the gun at the assassin, she has her eyes closed when she pulls the trigger.
When the villains' computer displays information about Kate the second time, for no reason a debugger window showing part of a C program appears onscreen behind it.
The online copy of Max's police ID gives his year of birth as 1965, yet shows the year this ID was issued as 1978. He became a police officer at 13?
The whole plot rests on Kazak and his men trying to kill Kate before her court case causes them to lose the Tortuga in the divorce case she is pursuing. However, they only need a couple of days to complete the transfer, and any court case Kate was undertaking would take weeks, if not months, before there was any chance her client would be awarded the ship.
Kazak's men try to kill Kate throughout the movie, but when they finally do catch up to her, they _capture_ her, citing that she has information that she needs.
The villains detect Max's cellphone in use, but do not try to monitor his conversation on it, even though they have demonstrated the more difficult capability of monitoring conversations on a conventional phone. By monitoring the cellphone call, they could have spotted Max's deception at once.
Thug on the Tortuga recognizes Max's voice over a cell phone, even though he'd never heard it before.
There is no such thing as a "heat sensor" which can provide a sharp, real-time image of people through walls.