My experience is somewhat limited to places that probably don't have the best developers in the world, but I think one of the major things I've noticed in people that I would consider to be mediocre programmers is a lack of desire to understand how something works. They just want to get the thing they need to work, and often times this lack of desire to understand how something works extends to their own code. If you strive to understand how your own code works, you will be much more likely to notice the bugs as you think through the flow.
Early on when I was learning to program, I had a very strong curiosity that made me want to understand how everything works. I think if you have that natural curiosity, it is the easiest way to become a better programmer. As I've gotten older, though, that has waned. In response, I've tried to build habits of investigating things and trying to learn about them when I don't understand them. It is tempting to just use google to find the answer, or "shotgun" it by trying all kinds of random things before you get it to work, but learning how it works is always the best, and it will pay off later.
So, I guess my main point here is to just keep tinkering and reading and getting your head wrapped around all these things so that you understand them well. Then things will eventually become "easy" and intuitive.