Practice is an essential part of our growth as musicians, and during that time our minds can be on a number of things. The real skill of practicing is to narrow our thoughts to work on specific aspects, one at a time, until the entirety of the work has been dealt with. Many of us may have not been taught how to practice, but rather have gone to lessons and been given an assignment to work on for the next one. How do we then take the assignment and work on it? Everyone's approach may be different but I think we have similar goals in common. Things like precision, execution, rhythm/tempo, consistency, sound production, and clarity are all something we inevitably work on, but how do we diagnose the issues, and more importantly, how do we fix them?
Execution and consistency are very similar. Are we meeting all of the necessary requirements, achieving the demands of the music, and is this accomplishment done the majority of the time it's attempted? The hope is that practicing will make anything we work on "stick" to the point that we can automatically execute and perform the piece with little to no issue. The more we practice, the more familiar it becomes and the easier it will be to execute. This is also where bad habits can be formed if one isn't careful. If we are practicing something incorrectly, we may very well learn a incorrect note, etc. So taking things slowly and being very thoughtful about how and what you are practicing will help prevent mistake in the learning process.
As a drummer, the first thing that I hear and listen to is rhythm and tempo. Metronomes will blatantly tell you whether you are rushing or dragging in the piece. If you hear the tendency to do either in certain sections, really isolate them to examine why. Often the reasons for either could be the ease or difficulty of a passage, so really paying attention when they come up will keep you grounded. Rhythm has a lot to do that as well. Perhaps certain things are compressed, and that causes the rushing, or the opposite (wide rhythms for dragging), but the precision of the rhythm is key when keeping a steady tempo. Really make sure that the notes have their full length and that will ensure a precise rhythm.
Sound production is the weird one. This is where we really need to take a step back and think about what we are doing that creates different sounds. As a percussionist, I know the main variables that will produce different tones: lightness/intensity of touch, length of time that the stick is on the surface, velocity of throw, weight given to the stroke. This could be translated as thinness or thickness of air, light or heavy bow pressure, air or bow speed, weight given to the bow, etc. Any combination of what creates your general sound will produce a different one, and really experimenting, finding out what is possible on your instrument and gets you comfortable with your instrument as well, even the bad sounds that it can make. Finding the sounds that you can use on a regular basis, memorizing them, and being able to execute them in any situation will give you more flexibility within any piece you play.
Clarity, I feel, is a combination of sound production and precision. If we are executing the notes at the correct lengths, the rhythm and tempo will be good, but if the sound we are using is not appropriate, the audience may not be able to hear anything you are doing. It could also be a case where the sound is beautiful and appropriate, but the lengths of the notes are not precise, things will not be clear to the audience either. So, making sure the sound is appropriate (if your playing a scary, soft piece, let the sound be dark and full but very quiet; not bright, thin and semi-soft), and making sure you can execute those sounds while giving the appropriate lengths and steady tempo, will make the audience hear everything you are doing. Spoon feed the audience the music.
There's probably a lot more that you can go into as far as examining yourself and your practicing, but I think this is the basic format that will get you to a very good place very simply. It takes time to develop a mind that can think of all of these things habitually, and also a method of taking things apart to deal with each of these problems, but take the time now. It can be frustrating, especially when you feel that you should be able to do these things already, or when you can do them only in certain circumstances. Really find out why they do, and what circumstances bring out the good and the bad. Only then can you dissect them and either recreate good moments, or get rid of bad ones. It takes time and even more patience, but if you take the time now, and stay level headed, not getting too frustrated, you will achieve the goals you set for yourself.