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 with the wrong style or wrong sound for a week it is much harder to get back on track than it is if you happen to have practiced something with slightly wrong notes. You can fix a wrong note quickly and easily by just using the correct valve or position but sound and style are much harder to alter and any 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 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 picture. Then as you practice slowly try and play in the correct style, with good tone, making the music come alive, just at a slow 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 'fairly easy' task of speeding it up to do and your good habits will help a lot towards it. If you practice something that should have lots of varied dynamics all at mezzo forte, then you will just get good at playing it all mezzo forte and actually be practicing 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 this 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.
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. Brass band contest audiences are a perfect example of this! Of course, the right notes are essential but you can really 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.