Suppose 95% of people with a certain disorder give a certain pattern of answers on a personality test, whereas 5% of mentally healthy people give that same pattern. if we use the test for identifying that disorder, under which circumstance will we make the most errors?

This question is a perfect example of the difference between false positives and false negatives. This hypothetical test is for all practical purposes, useless. Let's assume that the disorder is relatively rare and that only 1 out of a 1000 people have it and that we'll give that test to 20,000 people. Among that population, there will be:
1 person with the disorder who wasn't detected (false negative).
19 people with the disorder who were detected (true positive).
 999 people without the disorder who were detected (false positive).
18981 people without the disorder who were declared clean (true negative).

So we have a population of 1018 people who tested positive for the disorder, yet of that population, less than 2% of them actually have the disorder.