I've heard the GM advice to make failure interesting. I've even given that advice to people. It's good advice and worth adding to your game. I'd like to refine it, though, based on the most interesting failure stories I've heard. Sorry, I won't recount them now. You don't get my raw data, just my conclusions.
So, the old dictionary on my shelf says that irony is the expression of meaning using words which normally have the opposite meaning. I've also seen it defined as something that comes from an opposite or extremely unlikely source.
And that's what the most interesting play examples of "make failure interesting" are. A failed Circles test actually finds the contact, but they're hostile to you. The expectation is a good and useful contact, but it turns out to be a bad and (potentially) useful contact. A failed lockpick roll unlocks the door to - not the treasure - a room full of guards! The expectation is opposite to what happens.
There are plenty of examples outside these, some are ironic. Another substitute for interesting is complicating. Make failure complicating. Failed detective rolls succeed in identifying the villain, but at the cost of revealing your sister's identity to the villain. (FYI: Don't call around the crime world from her phone.)
"Interesting" is a broad term. I think it's more fun to make it complicating, and even more fun to make it ironic. It might wear thin after a while, so don't be a one-trick-pony about it. But try and make failure ironic.