A big mistake I see many pianists make is focusing on the wrong things and taking short term gratification over long term success. This can happen in all stages of our professional development--- from student to concert pianist to teacher.
When teaching or studying, we must always resist the temptation of doing what "makes us look good" instead of what will actually help our development. It is a very common situation to have a student that is particularly good at one aspect of music and almost completely useless in another (in my particular case, when I was just starting out, I had extremely good octave and chord technique but couldn't play a clean fast scale to save my life.) Many teachers will opt to ignore the problem--- sometimes on purpose, more often through self deception--- and have that particular student play repertoire that is easy for him, that shows off what he can do and hides his defects. In the short term, this will make the teacher look good since his students are playing so well, and it will make those students look good in front of their peers. In the long term, it's disastrous.
It is well known that the earlier we can fix problems with our technique, the easier they are to fix. By constantly ignoring them, or hiding them, we are making the problem harder to solve in the long term--- sometimes it becomes impossible to remove. In the same way, a teacher that constantly does this ends up having very few student who go on to become professionals, hurting him in the long run (not to mention how unethical it is to hurt your students in this way.) We are all guilty of this to some degree, but the those teachers that do it purposefully are like predators that take in students, use them up until their ability to make music is damaged beyond repair and then discard them for newer, undamaged students--- usually blaming them in the process for not advancing fast enough.
Another common problem with short term thinking occurs with those musicians that are fresh out of music school. I believe that self promotion is necessary. It is absolutely essential that a musician know how to conduct himself in society and the proper channels for obtaining opportunities to play and to teach. Even so, a lot of inexperienced musicians will neglect the quality of their playing and gaining new repertoire because they are too busy playing politics, presenting projects to every single cultural institution they come across, meeting up with patrons of the arts, festivals or concert promoters. What they don't realize is that by neglecting the quality of their playing in favor of trying to "get their foot in the door", once that big break comes, they won't be able to do anything about it and probably won't get called back. I firmly believe that, if you focus on making music as well as you can, everything else will eventually more or less fall into place, as long as you aren't going to the other extreme of acting like an isolated weirdo.
I've seen it too many times to count in my fellow students or in the ones I see graduating every generation. Imagine the case of a pianist that practically stopped learning new repertoire in the two years after he left music school. He spent all his time coming up with projects and trying to get concerts. When he finally got a much sought after audition, he played in a very mediocre way. They asked him what concert repertoire he had and that pianist could only list one or two concerts. He played a recital, and they never called him back again. In that same year, he got six or seven opportunities to work with other musicians and to give concerts but, they all fell through or they never amounted to anything.
In my case, I made that mistake early enough for it not to have a significant impact on my development later so, when I left school (which wasn't that long ago,) I tried to concentrate on learning as much relevant repertoire as possible and trying to fill up all the gaps left in my education. I didn't get so many opportunities and invitations to play in the first couple of years, but every single invitation I did get turned into a modest success which invariably led to other opportunities with the same institutions and with others, through word of mouth.
As a music student it is also very important to think of long term results. In the short term, it is easy to give up because we can't really see the progress we make unless we have some perspective. A lot of students tend to stick to a practice regime or to a different way of playing for only a little while and then, when they don't see quick results, they'll stop doing it. Many things affect how you play on a given day. You probably won't see results immediately when you practice, but as the weeks go by your average ability will always go up. Think of it like of following a diet. If you are losing weight, your weight loss won't go like this: 100kg-99kg-98kg-97kg-96kg-95kg-94kg... in a steady straight line decrease. Many things can affect it, how much water or food you have on a particular day for example. It will look more like this: 100kg-96kg-99kg-97kg-93kg-97kg-92kg... in a jagged line, but always decreasing on average. In the same way, if you follow a good teacher's recommendations, you won't see a linear rise in your abilities but, on average, you will get better.
It is simple really, to get good results in the long term you must be honest with yourself and with your students. As a teacher, always do what is best for the development of your student, even if it gets you criticized by your fellow teachers because your student's repertoire isn't as flashy or they aren't playing that many concerts. As a student, don't try to hide your problems, a student's role is to fix them with guidance from his teacher. As a professional, focus on making music as best as you can above all other considerations. I believe that by doing this, in the long term, it all works out.