When learning a new piece or working with students on new material I find it useful to try and shift my focus from merely trying to play the right notes. Of course, correct notes are essential, but if you practice in the wrong style or with the wrong sound for a week it is much harder to get back on track than it is if you happen to have learnt something with a few wrong notes. You can fix a wrong note quickly but sound and style are much harder to alter because bad habits get rooted very deeply. Many times when you see a student sight reading, their body seems tense, they play quite soft and articulate in a lazy, slower, more hesitant way. They forget about their sound quality, the correct style and get obsessed with reading notes.
Always start slowly with a new piece but make sure you have an idea of how you eventually want it to sound. Create characters in the music and let your imagination run wild with what the music makes you envisage. Then, as you practice slowly, try and play in the correct style, with good tone, making the music come alive, just at the slower speed. This includes, note lengths (relative to your speed, but taking into account the eventual note lengths appropriate to the style), dynamics, accents, articulations and all possible details. Despite playing slowly you can still play in the correct style with a good sound. This way you will only have the task of speeding it up to do and your good habits will help a lot towards that.
I like to challenge myself to learn a piece of music at half tempo first and give myself the added disciplinary challenge of not increasing the speed for at least one week. This will not work if I need to learn something quickly but I find in most cases, after that one week, I can normally play it perfectly straight away at the written tempo. Give it a try, and as always, adapt your practice to suit your own ability.
If you practice something that should have lots of varied dynamics but play it all at mezzo forte (mf), then you will just get good at playing it all mezzo forte and actually be developing your bad habits. Never practice bad habits, it sounds obvious but many students do this without realising. The same can be said when warming up or doing daily drills. Try and do them in a musical way and although some exercises require robot like precision, still aim to have emotion and character to your sound and the way you practice.
I get frustrated when I hear teachers asking students to simplify a task. For example, to learn a piece of music and ignore all dynamics and articulations with the plan to add them back in at a later stage. It is much better to teach yourself to juggle a few extra balls. You will become a better musician and learn things more efficiently if you focus on every single detail right from day one of learning a new piece. Even if the piece of music you are learning requires a very loud dynamic throughout, it is better to practice good habits and use that as an excuse to develop your dynamic range while learning the piece.
This idea can also be transferred to listening to music or watching live performances. Don't be obsessed with whether the performer has the odd slip but try and appreciate the music more, rather than listening for errors. Of course, the right notes are essential but you can appreciate music so much more when you think about playing with more style. Then as a performer, once you get the style and have an idea of some images the music creates, it is your job to tell the story to the audience. Body language, movement and how you look also go a long way with this so again don't just think your job is to play the right notes, music is much deeper than that.
Hope this helps.