Is it common got the gpus to die in these?
Since you didn't specify the model of your iMac G5. With the 1.8Ghz there's the
initial model with the FX 5200, and if my memory serves me right, that GPU has a very high failure rate among PC users (desktops and notebooks) and I can't remember if was considering filling a lawsuit against nVidia.
I have a
PowerBook G4 12" 1.5Ghz that was given to me by a dear friend, after a couple of months of use began the infamous GPU failing that appears very similar to your video.
The other
G5 1.8Ghz have the Radeon 9600 but I don't remember it having this problem (and I could be wrong), but every hardware it's prone to failure if don't cooled appropriately (and Apple don't have a great record in this segment).
Considering that the capacitor issues: Even if it doesn't appear leak of swallow, it can be failing, but only when you inspect or substitute that you'll find it.
Your possibilities are: 1)Capacitor failures. 2) GPU degrading. 3) GPU memory error.
Could have more options? Sure! But statistically that's the best bet's