Fargo

I don't ususally recommend police procedurals, but this Coen Brothers film is unique in several respects.  Officer Marge Gunderson (Frances Macdormand) has to solve a twisted, messy murder case despite experiencing one of the most distracting of conditions: she's extremely pregnant.  A key turning point occurs in the simplest scene: an old friend and coworker expresses his infatuation with her, and she lets him down gently while realising that the nicest people can be misread.  This inspires her to follow up on an earlier (seemingly benign)  interview with a frazzled car dealer (W.H. Macy) that leads to the eventual unravelling of the crime.  It's a study in empathy, which is at the crux of good investigative work.  But not all investigation films are this entertaining.