Here's an ENTJ one for starters (ENTJs probably have some of the most pervasive stereotypes around):
Myth: They are ruthless and power hungry
Truth: Um...that can apply to anyone - the above statement is probably worse than the best Forer statements in astrological horoscopes, since it is devoid of meaning in the context of ENTJ - Actually, ENTJs are inferior Fi types, so instead of this making them scary like so many stereotypes make this out to be, I've found no correlation to this IRL - instead, I've noticed that they tend to be anal about living up to a personal values system and tend to give in easily around upholding personal values if they aren't strong in this area - if they have control here, they tend to be rather all-or-nothing with it and get touchy when other people question them here (or at least they think they're being questioned here).
I'm not sure if you want to base your ideas of different types on stereotypes, because that could easily lead to assumptions about a person once you do know their type. I could give some examples:
Okay, the stereotype about T's is that they're cold and have stinted emotions or are not very empathetic, whereas the stereotype about Fs is that they're illogical. If you base your ideas on T's and F's on that, you can perhaps, easily be led to believe that a thinker is being cold and unempathetic when they're just basing a decision based on criteria that makes them feel more comfortable and vice versa....
The stereotype like Agent Blackout mentioned about J's and P's I believe is based on how western society sees J's as more desirable when it comes to how industries are run, etc., because everything has to be so fine tuned and tightly scheduled in order for a lot of major businesses to make a profit, so yeah, society will lean more toward the judging preference considering, based on that criteria that judgers are more responsible, when it's just based on, I guess an industrial definition of what it means to be responisible.
Then there's Ns vs Ss. Ns are supposed to be nerds while Ss are supposed to be dumb jocks, but, actually SJ types do better in school than Ns a lot of times, so they have to be smart somewhere. Actually both sensors and intuiters use the opposite function, quite often throughout their lives, so it doesn't really mean anything, except the mode of thinking the person feels more comfortable with.
Then, I find the biggest stereotypes are introvert vs. extrovert....Introverts, supposedly, are shy and wish they were extroverts, or non-social not team players, disliking people, etc. whereas, extroverts....again dumb jocks, lol, when all introversion and extroversion really says about a person is where they draw their energy and whether they're energized or drained by external stimulation....
So, what I'm saying is when it comes to stereotypes, even the most intelligent and rational person can easily be swayed by them so what I'm saying is just be careful and realize that people are way too complex to be defined by four elements.
I'm not sure what the stereotype for INFJs are, hmmm.....maybe the ohhhhmmmm chanting supercute spiritual sage on the top of an asian hill, spewing enigmas supposedly with deeper meanings. That's kinda my personal stereotype though
or maybe the crackpot heretic going around with encrypted messages portending impending doom
Correction: Since SJ are the majority, the school system was created by them, for them. Thus they will do better under the current school structure. I personally dislike it. I think it is rather constricting and does not allow room for any real creativity and thought. "Smart" is one of the most subjective terms and it irritates me to no end. If the school system catered heavily to iNtuitives then I'd bet SJs would have a much tougher time.