"Curate's Egg" comes from a Victorian Punch cartoon (see how educational this blogger is? As of several days ago, you know all about Punch, the Punch lunches, even the initials on the table of the Punch lunches).
Artist George DuMaurier drew a cartoon, entitled "True Humility" showing a nervous young curate eating an egg, at breakfast with a Bishop. The Bishop (who can smell the egg) observes that the curate's egg is bad, and the curate replies "Oh no, My Lord. I assure you! Parts of it are excellent!" But a bad egg is a bad egg. (I remember learning, with delight, as a kid, that you can tell if an egg is good or not by touching it with the tip of your tongue -- the tongue is sensitive enough that you can immediately find the warm spot that shows the existence of the little air-sac in the inner membrane at the big end of the egg, which, I learned from one of those "1000 Things A Boy Should Know!" books, isn't there if the egg has spoiled.)
As explained on Word Detective, DuMaurier's tag line, "Parts of it are excellent!", caught the popular ear at the turn of the century, and "a curate's egg" soon became a metaphor for a bad situation that someone persists in trying to salvage with misplaced or phony optimism. "A curate's egg" is still heard occasionally today, often incorrectly explained as meaning something that simply has both good and bad qualities. But that definition blunts the refreshing insight -- that Pollyannas are often ludicrous opportunists -- of George DuMaurier's classic cartoon.
Which is to say there's an underlying rottenness implied by "a Curate's Egg" that using it to mean, literally, "good in parts" doesn't get across.
Which means that the Neil Innes radio show isn't a curate's egg at all. Mea wossname.
Here's a bit of Mapping Mars, Oliver's book. Which is a very nice egg indeed.