Broadly speaking, it sounds like you're talking about making sure your designs are logically/algorithmically correct.
That's an honorable goal, but as Alan Perlis once said, "it's easier to write an incorrect program than understand a correct one."
Correctness is still something of a black art.
Most of the research in actual machine-assisted verification seems to be happening in the area of Formal Methods, but nobody seems to have come up with a real killer app in that field, yet.
Too many of the tools and notations out there use characters that don't exist on a normal keyboard.
In that sense, they're kind of like APL.. they say you can write any program in the world as a one-liner in APL, and in six months nobody, including you, will be able to read it. ;-)
Joking aside, though, you'd probably do well to dig through the literature on correctness and add as many of the general techniques as possible to your bag of tricks.
Three which I happen to like are:
Always design for zero, one, or many inputs.
Don't just assume an input's value will belong to a set of acceptable options, or fall within an acceptable range.
Try not to let invalid input force branching. Always return a valid, usable result, even for invalid input.