Can a psychological test have perfect specificity? i.e no false positives?

There is no test that I am aware of that has 100% specificity, psychological or otherwise. All tests have to be interpreted in proper clinical context in order to become relevant.

Standard psychological testing protocols always have some component of subjectivity, and results can be interpreted differently by two different psychologists. False positive issues do exist, and specific diagnostic outcomes are often elusive. Testing is often best used to correlate and substantiate clinical symptoms.