Say I'm in circumstance X and believe Y, and you're in X' and believe Y'..
I can try to understand what evidence you have for Y' -- that is, try to understand the subset of your experience of X' that is relevant to believing Y'. I can then use that understanding as additional evidence that informs my estimates of the likelihood of Y and Y'.
Or I can decide that I don't feel like putting that much effort into the question. Which is perfectly valid... as you say, this comes up all the time, and one has to prioritize.
In that second case, I can take various shortcuts.
Indeed, many such shortcuts are wired into my brain, and they aren't necessarily bad ones -- though of course experienced deceivers are used to subverting them. Others can be learned, either implicitly or explicitly. Some are so unreliable in the modern world I do best to _un_learn them.
What I try not to do is fool myself into thinking I've actually evaluated the situation when I've merely taken a shortcut. If I'm dismissing Y' and reaffirming my belief in Y without doing the analysis, the alarm goes off to remind me that no, that's not justified. Y is my current belief, and I'm choosing not to investigate Y' because I've got better things to do, and that's really all I can legitimately say.
In Anna’s recent post, she talked about training your mind to notice when it wasn’t curious about something and scream “Error! Look for a different way to do this” in such cases. Johnicholas and TheOtherDave's list of what stupidity feels like also looks useful for this purpose. I'm creating this post to make a more comprehensive list of feelings which indicate that people should reanalyze different possible paths to make sure that the one which they're taking is the most effective one to their objective.
Please suggest additions to the list in your comments -- I'll move them up here (along with links to further explanation, if given.) Keep in mind that your description of the feeling should be as illustrative as possible. For example, "feeling stupid" is unhelpful, while "you feel like you've taken a wrong turn into a never-ending tunnel" is better. Of course, metaphors which are immediately understood by some people may not be so easily understood by others, so try to give a more detailed description of the feeling if other people express that you're probably saying more than they're hearing.
List: "Error! Look for a different way to do this" if you feel like: