I've been thinking about this for a while now. Does the complexity of a system suggest a designer?
The increasing complexity of a system makes it much more probable that it has a designer, and that it wasn't created by chance.
Information, and thus complexity, requires intelligence, a la a designer.
Reminds me of nature and fractals. I'd say no until I see proof.
No. Not even a little. It is exactly what we would expect from a directionless, blind system. We're there a Designer, they would be fired.
Does the fallibility of said system suggest a fallible designer?
If there is fallibility, sure. But what one might define as "fallible" might be part of the complex system, part of the design, etc.