The Problems with Online MBTI

Feature Lists instead of explanations of the underlying principles in any rigorous manner. Sometimes the underlying principles are offered, but it is not explained exactly how they line up with the stated features. Feature lists are very bad explanations for the most part; it would be like saying that a bird is defined by a head, wings, feathers, etc. A pile in which a head, two wings, feathers, and all the other parts of a bird would fit a similar description, but would not be a bird. Rather, a good explanation includes these along with an account of how the features/parts fit together. This is reminiscent of Aristotle's matter/form.

With this comes an attendant disregard for the broader principles. Little time is given to Thinking or to Extroversion or to Judging, but plenty is given to Te. This limits understanding outside of feature lists.
This could be likened to those who try to make claims only about each individual type one by one, instead of explaining the functions.

Vague explanations, or ones that confuse a metaphor for a direct, literal explanation. For instance, when explaining extroversion/introversion, people explain them as 'external' and 'internal' focus respectively. This is both quite vague and mistaking a metaphor for a true explanation.
Objective orientation. People tend to take psychological principles as ultimately being about objectively real entities in some abstract or scientific sense. However, when we are talking about psychology, we're talking about people's experiences of things, not a theory about how the world is 'out there' - you know, the stuff that's going on in their psyche, the namesake of psychology.

Thus such an account of personality requires a phenomenological approach in some capacity. Not only does this better help to account for behaviour, it makes the theory actually useful in our lives, as it then is pointing out things that we can actually look for.

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