Alternative Character Interpretation: Is Melinda a well-meaning woman trying to help the living and the dead or is she just a nosy person sticking her fingers in everyone's pies? Some of the episodes seem to imply both.
Base-Breaking Character: Some fans see Delia as a Replacement Scrappy for Andrea and found it frustrating that it took so long for her to accept the existence of ghosts. Others liked the idea of a skeptic as a main character.
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Die for Our Ship: Nikki to some fans, because she gets in the way of Melinda and Jim/Sam, which however got better when Jim "returned".
Ensemble Dark Horse: Out of Melinda's many partners in crime across the series, Andrea seems to be the fan-favorite despite only lasting a season.
Henry Czerny appeared in the season 1 finale as a Federal Investigator looking into a plane crash. He would go on to play Conrad Grayson, a man who caused a plane crash, in Revenge.
In "Ghost Busted", Eli lies to Sam/Jim about Melinda being an FBI profiler. Both Jennifer Love-Hewitt and Aisha Tyler played FBI profilers on different seasons of Criminal Minds.
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Jerkass Woobie: Pete Murphy is a downplayed example, as he's still just a little kid, but he's very obnoxious to Melinda and was apparently very troublesome when he was alive.
The show got a reputation for all the ghosts of the week appearing villainous but always being revealed to have been misunderstood or innocent. While that does happen a lot, there are plenty of villainous ghosts. Notable is "Friendly Neighbourhood Ghost" where the old man turns out to have been an abusive parent, and "The Last Execution" where he confesses that he did commit murder.