Bizarro Episode: "Transylvania, January 1918". It comes out of nowhere and even years later still makes no freakin' sense. (In the original, never aired cut, the Transylvania episode was told as a ghost story by the old Indy to some children in Halloween. So there was the possibility that it was completely made up. But then the new cut had to screw it completely...) It does, however, feel closer in tone to the movies which often have supernatural shenanigans and goings on.
Fanon Discontinuity: Some fans of the movies prefer to ignore the TV series. However, the re-cut of the series (which does away with the frame story that causes most of the tension) has been better received.