If anyone can find me a factor analysis which found that 1) there are only four factors which describe all variation, and 2) that each axis is orthogonal, THEN we can begin considering the validity of the MBTI, but as it stands, the construct validity of the entire thing is deeply suspect.
Here is a study that found six factors, rather than four, and there's evidence to suggest that the J-P and S-N scales actually correlate with each other. If you have even a basic grounding in statistics, you should understand why these alone are pretty damning. It would fail both criteria I outlined above, which are pretty necessary for the test to actually do what it reports to do.
Furthermore, despite the claims that MBTI describes some kind of cemented personality type with carry from cradle to grave, there's pretty strong evidence that your type changes depending on your mood.
Researchers found that, when taken 5 weeks apart, 1/2 of subjects will get a whole new type. You may be an INTJ today (and that's what you may want to be), but that doesn't mean that's what you'd get if you took it tomorrow. That link takes you to a pretty good breakdown of all the criticisms of the MBTI, and they're all very well thought out.
And given how easy it is to 'guess' what the 'correct' response is to get the type you want, why should we believe it's objective at all? Even if you're not consciously cheating, unconscious bias is still a real thing.
Let's also remember that Jungian analysis (like all psychoanalysis) is fundamentally flawed. As much as people seem to love the *idea* of psychoanalysis (God only knows why...), it's not based in any kind of science. It's not readily testable, it's not easily falsifiable, and it's based in the philosophical ramblings of a lot of old dead white men. Although I know how much we love philosophical, old, dead, white men, so I'm not all that surprised. Let's remember that Jung and Freud never TESTED any of this - there's no predictive power here. They just said "hmm, this makes sense, given my preconceived notions and biases, let's call this truth."
If you're interesting in quantifying personalities, the Big Five is a lot better than the MBTI (although it's still got a lot of conceptual problems).
Anecdotally, I feel like a lot of fans of the MBTI are less interesting in having a useful and consistent model with which to explore human behavior and cognition, and lot more interested in the auto-erotiscism inherent in comparing their types and talking about themselves.
Blessings
~ND