The only one I can think of off the top of my head was that the "arm" that holds the LCD display up would sometimes get loose over time and not stay in the spot you would move it to. It was an easy fix though - just tighten some screws I believe. Other than that, the iMac G4 was a pretty trouble free machine.
Oh yeah and if you buy one used, make sure to take a vacuum and suck out all the dust that will probably be clogged in the vents under the base.