tl;dr - The issue of the MBTI and psychometrics in general is nuanced, and strongly held opinions of either pseudoscience, or devoted metaphysical truthiness, are equally problematic.

The MBTI test as it currently stands, deserves the reputation as flawed empirical instrument, yet at the same time it's utility is undeniable. Unlike horoscopes, individual descriptions do differ rather significantly. The biggest issue in my view is not a fundamental one, but rather a flawed set of assumptions. The principle being that the test taker, possesses intimate self knowledge and presents an accurate and unchanging self portrait. In addition to the wonderful qualities humans have, there remains a number possible impairments with regards to self assessment: bias, delusion, deceitfulness, fancifulness, ignorance or simply an innocent unrefined skill in introspective ability. Thus the issue appears to largely be with the test itself, and not so much any solid refutation of the Jungian theory on which it rests.

While Jung certainly had some strange and mystical ideas, which would be difficult to support in today's scientific environment, his theory of cognitive functions is uncannily prescient IMHO, and believe is most deserving of further scrutiny. He is also largely responsible for the introducing the concepts of extraversion/introversion in the early part of the last century which have remained a mainstay on both public and academic discourse. [5]

Thus upon reflection, the observation of Jung as a mystic, is not necessarily an indication of a weak mind. One should not overlook the fact Sir Isaac Newton, perhaps one of the greatest scientists of all time, had strong mystical[1] and occultist[2] leanings too.

One might argue "well, the 1600's are quite different to the 1900's and Jung ought to have known better". Yet if the whole idea of a personal God seems rather delusional in the 21st century, the fact that credible scientists continue to partake in it today, does not simply invalidate their scientific discoveries. For example, James Smalley's [3] won the Nobel prize for the discovery of Buckyballs while simultaneously being an ardent supporter of old earth Creationism. Another example would be notable Christian apologist and Human Genome Project pioneer, Francis Collins [4]).

Returning to the issue of the test itself, the primary concern is that it it relies on self-report and is not a direct measure of the physical cognitive diversity existing between brains.

On the topic of Jung and neuroscience there is some preliminary proto-research by done by UCLA researcher Dario Nardi investigating the possible evidence for Jung's cognitive functions within the brain. He gave a talk at Google in 2011
http://www.youtube.com/watch?v=MGfhQTbcqmA explaining his results.

Of course this is by no means an empirical vindication of Jung, but it does open up a potentially interesting line of exploration. As with any non-peer reviewed work, it should be treated with due skepticism.

Lastly, for those interested in further reading, I have digitized a copy of Jung's seminal work, 'Psychological Types (1921)' [5] am sharing it for anyone wishing to study the source material.

[1] http://en.wikipedia.org/wiki/Isaac_Newtons_religious_views

[2] http://en.wikipedia.org/wiki/Isaac_Newtons_occult_studies

[3] http://en.wikipedia.org/wiki/Richard_Smalley

[4] http://en.wikipedia.org/wiki/Francis_Collins#Christianity

[5] http://books.google.com/ngrams/graph?content=extraversion%2C...

[6] https://www.dropbox.com/s/hrf6whb66fbmaux/Psychological%20Ty...