1- A musician who plays faster or someone who plays complex things does not make him a good teacher: A common mistake is to believe that by studying with a specific person will make you like him. It's easy to get confused and I think it is an important factor to consider because not only the things that I already mentioned happen but also you can discover that many excellent interpreters use the pedagogy as a means of subsistence avoiding the importance of this job, for instance, guiding a student by giving the appropriate resources in periods of time through precise and adapted planning for skills and also, potential the learner developments (and ideally aligning with their objectives: 3rd mistake).
2-Thinking that an institution has "famous" students is a good one: In Chile, music institutions lie, the prestige of each musician depends not only of their work but also on his ability in human networking (lobby), marketing, production, etc. All institutions can boast about the achievements of their best-known students: that does not mean that they have made some extra effort to get their students there. On the other hand, the fame itself has nothing related with the musical value, discipline invested in music, work done, and its quality. (This statement is for another post).
3- Lack of research:
To research you must be clear about what you want: if you want to make music or if you want to make music and earn money. Knowing that answer, the next step is to understand the music paradigm (how it works, which ones are your options, which of them are paid and what are the real possibilities to work). After considering those points, the teacher or school always has a mission and vision (who they are, where they come from and where they are going; who does not have this clear as a pedagogue is not worth it), with that you can compare and contrast the information with your own interests and finally make a responsible choice, informed and above all, that could be aligned with your true musical purpose.