Audio problem: Right after Det. Corelli finds the limerick in her apartment, she pulls out her gun and there is a distinct sound of what's supposed to be her cocking the hammer on her pistol. However, Det. Corelli (along with all the other cops in the movie) uses a Glock semi-auto pistol, which does not have an external hammer that can be "cocked." The sound is added artificially, likely for dramatic effect.
Other mistake: After the main characters are talking in a bar, the camera shows a wire above a street. On the wire, there are 3 pairs of old shoes hanging by the laces. However, a closer look reveals that 2 of the 3 pairs are NOT actual shoes, they are just cardboard cut-outs printed to look like shoes and they have the same graphic.