The opening sequence (set pre-2000) contains a shot of London, including the Houses of Parliament, with a black-roofed building opposite (which, in fact, was not built until 2000). Later during the movie, now set in the present day, a similar shot correctly shows this building under construction, with bare foundations.
(at around 1h 26 mins) When Mary holds the knife in front of Dracula, saying she wants SImon's head, the curve of the blade changes direction from one angle to the next.
At around 41 minutes Simon shoots Nightshade 3 times after Van Helsing shoots him once but 6 bolts appear in Nightshades chest.
Van Helsing's office building is in London, but the Security Guards on duty are armed. Security guards in the UK do not, and cannot, carry guns. Handguns are illegal in the UK and private citizens, even security guards, cannot possess handguns, much less can they carry them about. Handguns can only be carried by the armed forces and by specially trained police officers (and even then it is rare to see an armed police officer).
In the opening scene, there is a Serbian flag at the ship Demeter. However, Serbia at that time had no access to any sea, and consequently no ships in possession.
This version of Dracula is said to have not only been Vlad the Impaler but Gilles de Rais. He'd have had to be in two places at once because they lived at the same time.
(at around 1h 15 mins) Lafayette Cemetery closes at dusk (or maybe noon, reports vary); the gates are closed and locked. Yet we see the gates stand wide open very late at night.
(at around 1h 30 mins) The sidewalk that Mary lands on near the end of the film visibly vibrates when she hits it.
(at around 1h 7 mins) When Lucy (Vitamin C) grabs Mary (Justine Waddell) her left contact lens moves out of place.
(at around 20 mins) When Nightshade accidentally cuts his finger with the chisel, there is visibly no blood on the coffin. Yet it shows the coffin sucking in the blood 'from his finger.'
(at around 1h 8 mins) In the long hallway scene at Mary's house, the female vampires are crawling on the hallway walls. Mary has her back against the wall, however, its obvious that the scene is filmed with Mary lying down and the camera rotated for the effect. As she turns her head her hair falls backwards, towards the wall.
Simon being approached by 3 women vampires holds up a wooden cross but it has no effect.
In a partly crowded street Simon walks along looking for Mary yet moments later a shot looking down from the roof tops shows the streets empty.
The detonation of the wall inside the vault should have blown the rocks and stone outwards, not inwards.
(at around 1h 14 mins) When Dracula throws Simon across the room in the library, you can see the cable attached to him.
Van Helsing kept Dracula imprisoned because he couldn't figure out how to kill him. Yet in the end exposure to sunlight (a well-known method) did the trick.
There's a crucifix in the coffin and others on the lid to keep Dracula imprisoned yet later a large illuminated cross has no effect on him.