Solid capacitors burst, PC seems fine, how safe is it to keep using it?

I would not recommend to use this card and would replace it immediately.

It looks like you're not the only one - does this look familiar?

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If it's running fine now, it'll probably stay running fine for a little while. Eventually after another one fails the screen will get all squiggly looking, then the next one will fail and your computer won't boot...

I recommend replacing the card with something else. We've had probably a dozen Nvidia cards fail that way here. I've repaired a couple of them by replacing the blown caps, but eventually other parts on the card end up blowing up too.

I'll even go further and say that anyone with an Nvidia 8600 should just go ahead and replace it now. If it hasn't failed yet, it probably will pretty soon...

It's safe to use, for now. It might BSOD at random, but if it hasn't yet, it might not. You could try replacing the capacitors yourself, or just use this as an excuse to upgrade. I've known people use laptops with blown capacitors for years without there being an issue, but I've also known cases where it killed the PC, so YMMV, but it seems like you should be fine.