Human reasoning can be thought of as a process for moving from ignorance or doubt to knowledge or firm opinion. From this perspective, our human reason can fail in two major ways*:
We can overreach, so to speak, by arriving at a wrong conclusion.**
We can underreach by not arriving at a right conclusion.
We can cut down on our tendency to overreach by disciplining our reason, to notice when we're treating guesses as facts, possibility as proof, or preference as evidence. The more comfortable we are saying, "I don't know," or, "I don't have a strong opinion,***" the easier it should be to avoid overreaching.
The likelihood of underreaching can be reduced by training our reason, to understand insofar as we can the different ways we can reach the right conclusion starting with where we are now, and by learning what we can about the subjects we need or want to reason about. It seems to me in particular that knowing how to apply reasonable arguments from authority may often help you get into the neighborhood of the right conclusion on a question for which you don't have good personal knowledge to start with.
*There are truths that aren't accessible to human reason, but not arriving at these truths by human reason shouldn't count as a failure of human reason, any more than not telling you what to have for dinner should be counted as a failure of your toothpaste.****
** I'll count getting lucky -- reaching the right conclusion despite improper reasoning -- as overreach, if only because you wind up with false knowledge about the basis for your conclusion.
*** I am strongly of the opinion that people should say, "I don't have, need, or want a strong opinion," a lot more often than they do, even given the selection bias of usually not noticing when people say that.
**** Of course, our human reason can still fail when applied to truths that aren't accessible to human reason. We might overreach, by concluding that an inaccessible truth is accessible, or underreach, by concluding that an accessible truth is inaccessible.*****
***** This sort of thing is why most people don't reason about reason very often.