OK, here's the Tokien version: *Big sigh from crowd* If you look at what Zuko has tried to accomplish, then yes, he IS a failure, even though he has done some spectacular things. (My favorite: infiltrating the very spiritual center of the Northern Water Tribe by swimming under the entire place in near-freezing water.) He has not captured the Avatar, or even detained him for very long. He has gotten his butt kicked a few times.?? He has utterly failed to impress his father. He has, so far, failed to become a master firebender.
The Tolkien explanation is that Zuko has another, bigger destiny. In LOTR, each character, even the seemingly incompetent ones (Pippin!) had a destiny to fulfill, but sometimes their destinies were quite different from what they had envisioned when they first set out. That's true in a lot of great fantasy stories. Zuko fits into that category. He has failed so far because he's fighting his instincts and his real destiny tooth and nail. We know he thinks his father is up to no good; he said so in episode 3. We know that he kind of likes Aang, and even envies him; he tries not to because he's been trained from birth that the Avatar is his mortal enemy. He's seen first-hand what happens when someone tries to mess with spirits (of which the Avatar is the chief) or the balance of the universe. So, now, he gets to wander around for a while, start to see things through his own eyes instead of those FN-colored glasses, and he'll eventually figure it all out. But it'll be a bumpy ride. Which, of course, is what makes it so interesting.
Just to top off my rambling, here's my favorite poem from The Lord of the Rings:
All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be King.