I think that only real thing that is wrong with MBTI are functions. To be exact function order in each type. I think it would be better if functions are treated as something like the ennangram.
I mean this forum is full of people who don't fit in the model. (myself included)
I agree. However, you have one misinterpretation here.
For example INTJs have Se are fourth function but ISTJ have don't Se at all in first four. What would mean that INTJs are better in Se then a sensor.
Unless you say that ISTJ Se is still stronger then INTJ Se, even if that if is a function that is not in the first four for them.
Another example is in ESFPs and ENFPs
They don't have Fe in first four but from what I have seen they have a fair amount of it. How it is possible that ESFPs are so much "fun, fun" type but their Fe is nothing special? In a way INTPs should have stronger Fe then them. What I don't think it is the case. Another thing is that they have Te. It is somewhat apsurd that that extroverted feelers have stronger Te then Fe.
The tertiary and auxilliary functions are not actually supposed to be your third and fourth place functions, they are supposed to be your 7th and 8th. So primary and secondary are the top layer, and tertiary (misleadingly named) and inferior are the bottom layer, and the four inbetween usually aren't mentioned. The reason for this is based on the crazy shadow theory and how your weakest functions bubble up and often have more influence than any of the four above them in times of stress (that was a very sloppy simplification, by the way). So technically, that the INTJ has Se listed in the four and ISTJ doesn't, actually implies that the ISTJ does have more Se.
But ultimately...
Agreed.. the models try to explain too much sometimes. The primary and secondary functions seem to be the only ones that are consistent across those of a particular type, and that's pretty much just by definition.
...This is still right, as far as I can tell. With my design of the Enneagram, I proposed a method for finding an order of preference, but me and Evan did both conclude that assuming that the full order could be charted out is just unreasonable. I might even go so far to say that the first three and the last three can be determined, but the middle three definitely cannot.
The MBTI has a similar problem, though I'd say it's slightly worse, since I don't believe you could even predict what the least used function is. As greed said, the first two functions match, but essentially by definition. It's analytically true. The remaining function orders, however, are supposed to be included as something synthetically true, but there is no logical warrant for including them.
Again, we can go to the Enneagram as an example. Me and Evan scrapped the lines of disintegration and integration because they seemed to be wild assertions. It was hard to figure out what other part of the system really supported that part of the system (and if there's no inter-support, it's almost definitively
not a system). Which brings up perhaps the biggest flaw with the lines. They described a transformative process. To my understanding, these type systems can never be trusted to do that. They can measure things, they can described them as the measurement showed, but both are static reports, they are not speculation about transitions. The Enneagram lines, and also the MBTI shadow functions, attempt to predict the nature of a transformative process, and when it does that, it immedietely stops being descriptive and becomes perscriptive, which, you know, means it basically becomes zodiac. Assessments about the remaining functions are essentially divination, like numerology, or Freud's weird-ass psycho-analysis.
EDIT: I've just realized this post is a mire of pedantic and esoteric terminology.