Maybe you're right. Where did you get information about poor reliability and accuracy though? And how do you actually go about measuring its accuracy.
I got it from the numerous studies that have studied the reliability and validity of the MBTI. If a test is truly consistent and reliable, it will stand up to the numerous methods, as described below.
In terms of accuracy, we would be talking about validity, not reliability, as a test can have high reliability, but poor validity. Meaning, you can get the same results over and over again (reliability), but not the results you necessarily want (validity). Remember, a test can be reliable (consistent) without being valid (accuracy).
So, you go about measuring the validity and reliability of a test through a variety of means, such as test re-test reliability, alternate forms of reliability, inter-item correlations (internal consistency), inter-rater reliability. As for validity, there is criterion and content-related validity and you go about measuring these through models such as predictive or concurrent validity, etc. No personality test is 100% accurate, but the MBTI is horrible in this regard. These are ways in which one would measure the accuracy/consistency of a test and before the establishment of any assessment measure, there is a process to ensure the test is reliable and/or valid (this goes for any scientific assessment measure).
The MMPI is probably the most widely used and accurate/reliable measure of personality, as it has has shown consistency and accuracy across numerous populations.