And because of this, one more option is to explicitly limit the amount of time the computer has to "think."

This option is both subtle and powerful. To use the chess example once again, the likelihood of a "missed brilliancy" is not a lot lower than that of an ignored blunder. Perhaps somewhat lower, since the brilliancy may have already been discovered in a prior move, but if I'm forced to think fast, the likelihood of errors increases a lot.