Reddit mentions of Jung’s Personality Theory Quantified

As far as the "there are no good tests," if you look at MBTI preference scores as continuous traits (as the Big Five does), then the test/retest of newer versions of the MBTI are about as good as the top Big Five instruments. The issue with test/retest comes about by treating the axis of the MBTI as dichotomous. Even the main researchers who developed the Big Five thing the MBTI is pretty decent.

I'd also recommend you look at Reynierse's articles in the JPT (there's a decent summary page here), which point out the there's no empirical evidence for type dynamics (despite people looking for such evidence). He recommends an approach which takes into account preference strength, since middling preference scores have little predictive or descriptive value.

In addition, there are more than a few MBTI-based studies, although not nearly as many as there are for the Big Five. Since four of the Big Five traits correlate reasonably well with MBTI preferences, one take take in Big Five studies, keeping in mind things may not translate exactly.

Lastly, Wilde, building on Reynierse's ideas has some up with a system for recovering something like functions using quantitive strength of preferences (there's also a visual calculator). I do wish his book wasn't so expensive, though.