The main criticism that Jungian typology theory has always encountered is that, as of 1921, it had not been tested thoroughly nor using the scientific method. Upon reading more information on Carl Jung, most critics agree that a lot of his work was empirical, as it is mainly based on personal experiences.
This being said, this philosophical foundation is the basis of the Myers-Briggs indicator. This means that Myers and Briggs used this untested theory as their research rationale to build an assessment tool that will correlate jobs to personalities.
Moreover, Myers-Briggs has been found to lack enough evidence for correlation in the dimensions of extroversion and introversion. Furthermore, it does not have as much empirical and quantitative data to support its validity 100% when compared to other personality tests.
Another common criticism of personality tests in general is that the data that is collected depends entirely on the honesty and self awareness of the tester. Hence, someone with a disparate notion of their personality may enter information that is entirely wrong, thus invalidating the results of the test.