The newspaper image (appearing to be an actual news image) depicting the bloodied female bodies are dressed differently to what the victims wore prior to their deaths. Also the likeness of the female victim does not resemble either in the film. The image of a male corpse does not appear to have found dumped in a drainage as mentioned.
When Inspector Lui request Ling to search on Min's apartment for evidence including medicines; he would not need to do that as a police inspectors have access to a search warrant. Had he done that, Ling would not need to put her life at risk.
Inspector Lui revealed to Ling that Min's grandfather was given the same poison as his murder victims. As a police inspector, knowing of his work and school background, Liu should had known Min lived above a medicine shop and therefore have easy access to the medicines. So why does he need to ask Ling to search for evidence of medicines in his apartment, are police inspectors not that bright?
The policemen have exceeded the number of bullets they've fired from their service revolvers.
When Inspector Lui interviewed Min in his office, Lui indicated to him that all three of his victims were given the same poison as Uncle Kim. Whilst the latter was poisoned via snake bite, unlike the others. An autopsy would had indicated that; a fact not indicated by Lui.