Other mistake: When Martin Harris is being chased in the taxi, paint covers the entire screen. Martin asks for the wipers to be switched on, but by the time the taxi crashes, the windscreen is completely clean, with no sign of the paint. There would be wiper marks and the remaining paint on the windscreen.
Other mistake: In the first scene, Liz and Martin are driven in a taxi from the airport. The driver is on his mobile phone. The subtitles say that he is speaking German, however in fact he is speaking Turkish.
Answer: Because the killers need to make Liam Neeson's death look accidental. The police think Neeson is crazy, and is not telling the truth when he claims Liz is his wife. The police simply think that Neeson is mentally ill and so dismiss his stories and allegations as untrue. However, if Neeson is then found murdered, there is the possibility that the police think Neeson might have been telling the truth, investigate, and foil the villains' plot. Therefore, Neeson must be killed to stop him investigating - but he must he killed inauspiciously, so it looks like an accident, so as not to make the police suspicious. Thus the poison in hospital - hopefully it would be put down as a standard non suspicious hospital death. And the drugs in the car park at the end of the film are deliberately mentioned by Professor Rodney Cole as being essential in making Neeson's death look an accident. Cole says that Neeson will seem to have killed himself with heroin and so will not consider his death suspicious. So basically these elaborate ways of killing are in order to make Neeson's murder seem an accident and so not make the police investigate.
swordfish