Well, as there are many students learning many different instruments each with their own individual challenges, I feel that I may not be to fully answer this question. However, I will give my best shot. These are not in order.
Bad technique habits. Especially for self thought players, bad habits formed earlier may hinder or impede technical proficiency later on. Usually overcome with the help of a teacher or through studying ones own technique to identify bad habits.
Too much tension. I think this can apply to most instruments. Tension in the body makes it much more difficult to play smoothly and with a high amount of dexterity, and may also cause long term physical damage. Even worse, a player may get used to it and will perceive the tension to be normal. Awareness of ones own body is important to identify muscles that are tense and to find ways to release the tension.
Bad practice techniques. This includes, but not limited to: trying pieces that are to hard, trying to speed up when you're not ready for it, not playing slowly to avoid mistakes and ingraining mistakes into the mind, etc. A good teacher can help, but there are also many books and even online articles on how to maximize practice. Remember, perfect practice makes perfect.
Untrained ear, unable to use the ear well. A problem for all musicians, especially string instruments and singers, and for anyone wanting to play in a style that involves improvising (jazz, blues, etc.) A good ear can tell if a note is in tune, what a note is in relation to other notes, identify chords, etc. Needs to be developed through ear training, either with a teacher or with an online trainer. You can search the internet for ear training exercises.
Lack of motivation/discipline. If you don't deliberately practice regularly, then achieving any level of proficiency is a distant dream. Remember, a little everyday adds up to a lot over time.
No sense of pulse/rhythm. If a player cannot feel the pulse of the piece, no matter how much you tap your foot, you will get lost. Working with a metronome is your best bet (or a drum machine for some variety).
I think these are some of the common barriers to musical proficiency. I chose not include factors that are out of the learners control such as physical limitations, no time, etc. Others are free add anything that I may have left out.
Daryl L