Rockgran: In a round-about way, I think you have hit on the reason why "the cake turned out good" sounded ok-ish to me. I definitely interpret it as shorthand for "It turned out to be a good cake". In other words, I see it as a description of the end result, the cake itself, whereas "it turned out well", to my muddled brain, says more about the action leading up to that. I'm not saying that my reasoning is grammatically acceptable (and from all the answers, it seems that it definitely isn't), but simply that I've now managed to work out why both seemed possible to me.
Thanks for all your answers, everyone 