When teaching, tell students what TO do as opposed to what NOT to do. I constantly hear teachers telling students negative commands: Don't tongue sloppy, Don't breathe there. How much easier is it to learn when a student hears: "Try tonguing like this" (and then show an aural example and explain what you are doing) or " Consider breathing here because the phrase is longer, if you need a catch breath, try this spot instead." Another positive comment about breathing might be "consider playing softer so you can make the long phrase and as you get confidence, play a little louder". Notice the difference in your own reaction to reading a negative command based statement versus a positive solution based statement. Good teaching is positive and supportive, and does not break down the student. There are times to 'wake up' a recalcitrant student, but again, keeping it positive and kind is always the best choice.
Vibrato is a characteristic of flute tone, and styles of vibrato change with general shifts in musical taste. If my ear is drawn directly to vibrato, there is usually some kind of problem: maybe the vibrato is forced (produced with a closed throat) or it is too wide and disturbs the pitch. Tasteful vibrato often depends on the musical result desired, but in general, vibrato is integral to the tone itself. It enhances the beauty of the tone and does not draw attention to itself. Vibrato gives spin, color and motion to the more static notes: i.e, we don't generally vibrate on moving 16th notes. I find a slightly more shallow vibrato that is also a bit slower is useful to aid projection in tutti orchestral passages: a more tightly wound vibrato is less appropriate in this circumstance. And sometimes on big tutti chords, no vibrato is the correct choice.
Think of vibrato as a musical paintbrush and apply different intensities according to the musical demands.