The list has actually grown quite a bit over time, and some of it may be viewed as controversial, given that we are in a typology community here.
First, type by itself can be limiting to yourself. While it can serve as a guideline to self-development, it can also set restrictions, and it's definitely possible that you forget some aspects of yourself that aren't covered by your chosen type. Over time, I noticed that some people simply cannot be boxed into a single type, their interests are too diverse and multifaceted to detect a clear hierarchy structure that could determine a type. If you would try to pin down a type, you would instead observe a pattern of type-switching or ambiguous preferences. It's not a common things but it does happen.
Second, like [MENTION=22833]Legion[/MENTION] already mentioned at the first post, is the different perception of other people. While type can be useful for a quick classification of other people, there are a few problems with this: Your own perception of someone's type can be wrong for various reasons (like misjudging, or the other person masking, or by judging someone based on their group they belong to). Also, type as a framework doesn't tell anything about a persons interests and what they prefer. An INFP, for example, might judge ethics based on their internal value system, but you can't say what exactly their values are. And, lastly, what I mentioned at first, type may not be accurate for that person at all.
My third point is stereotypes. The difference between type and stereotype is that type only provides the framework for evaluating people, while the stereotypes try to expand that framework into everyday examples. The INFP example above also fits in here, but there are some other examples: Feelers are stereotyped as female, and thinkers as male. Procrastination is seen as a Perceiving trait, even though it is present in [unhealthy] Judgers as well. Extroverts are portrayed as sociable party-animals, but extroverts who don't like parties definitely exist.
4th and last point for now: The validity of the theory. I think
reckful's takedown on type dynamics should be a mandatory lecture for anyone applying type theory. Not agreeing with him is fine, after all I believe that critical thinking is something everyone should practice. There are good arguments for and against the validity of type theory, and ultimately, it's up to you to decide whether it's valuable or not. There is a similar amount of criticism about other personality theories such as the Big5. Or MBTI's dichotomies. Often, Big5 is referred as being "more scientific", but what exactly is scientific?
About overcoming typology, I guess it is valuable to expand to other areas of psychology, and some philosophy, maybe spirituality as well if you like it. Try to look beyond the scope of type, develop a different pespective. It's a huge, complex field. You could start at the stereotypes, look where they come from, and what may be other, no-typology related reasons for it. Who are the depressed artists, the procrastinating computer geeks, the party people, the boss people etc, this time not from a type perspective. You may want to look at people who are different from the norm in a substantial way, like autists or HSP's. What is their perspective, how do they perceive the world, what makes them tick, how do they deal with the differences? And maybe take a look into some philosophy as well, what is important in life, what should we strive for, what is valuable? Sometimes I see type as a simplistic, comfortable shortcut to answer larger questions.