sounds to me like the wires are switched. Instead of actuating the left turn signal you are actuating the parking lights and the rear running lights via the flasher. This is the only way both front and both back can flash off the turnsignal that I can see( check to see which filiment is actually lighting). I'm not a eletrical guru but if all lights are flashing then there is a common wire to them all and in this case it doesn't really sound like a bad ground to me. Sounds like a direct wiring issue.
