We all remember that basic fingering chart we saw in our first method book or band folder. Fingerings can move beyond those basic ideas at the advanced level. Try adjusting the pitch of third octave notes by using the C# paddle key on the foot joint...many times just sliding over to this key instead of the usual D# key on the foot will raise the pitch just slightly ...useful on notes sustained at the piano dynamic. Check pitch carefully on third octave Bb and B natural: sometimes lifting the D# pinky key will adjust the pitch in EITHER direction, depending on the specific flute you are playing.  Try raising the pitch of any note fingered with the LEFT hand by opening the G# key. (any note except G natural however...otherwise you will get a g#). Keep your tuner handy as these are subtle adjustments. 

How many times have you (or your students) played a passage perfectly at home, yet made errors during those times that matter...ie, in a lesson, performance or audition? It is human to err, of course, but secure tools to build consistent technique can lay the foundation for nearly flawless execution all of the time. To be confident about your technique, both accuracy and repetition are your best friends. It's important when you break a passage apart to GET IT RIGHT...this means articulation and dynamics have to follow the printed markings too...this is game changing for accuracy. As for repetition drills, there are many strategies: some of my favorites are to play a passage at a reasonable tempo, speeding up one mark on the metronome, then playing the same thing 2 notches slower on the metronome,  then one mark faster, etc. alternating back and forth. I have great sucess by varying the rhythms, which changes the emphasis of finger combinations in a passage. Breaking the passage up into smaller pieces (ie, chunking) is also a terrific way to fix problems. Often it's only a two note finger combination that produces the stumble. Make every practice session a labratory for success, and try out these simple solutions for technical success.