Warning: I'm mostly an "Inner Game" guy.
I consider analysis of mechanics to be something of a Pandora's Box.
Item #1: Bounce Backs
Here's one I see often: As a student plays a downward leap I watch their embouchure. Often I see an adjustment, especially for leaps to low notes. Not, in itself, a bad thing (depending on what kind of adjustment we're talking about).
However: I often see the embouchure make too big an adjustment and then "bounce back." Basically, I think the "less is more" or "quiet down the embouchure" approaches are good here. Try the following leaps...
Look in a mirror as you do this. You may notice that your embouchure over-adjusts for the leap and then has to bounce back to a more centered position. In your sound, you may hear this as a scoop up from below the pitch.
Item #2 Pull Aways
I observed something odd in a lesson today. I have often buzzed a note on my mouthpiece and then, while continuing to buzz, gently placed the mouthpiece into the horn.
Try this buzzing an F-sharp and put in the mouthpiece while the horn is in first position. You'll end up with a very pinched F.
I've never done the opposite. Play the note on my trombone and then, while sustaining the buzz, pull the mouthpiece out of the horn.
When I did this on a low B-flat, big surprise, the buzz magically floated up to roughly a D-flat.
What caused this? Am I aiming too high?
It was easy to make a small adjustment to retain the B-flat pitch, by the way.
You might logically conclude that I could buzz a D-flat and return the mouthpiece to get the same sounding B-flat. Nope, just a really foul, uncentered something.
Incidentally, this effect doesn't seem to happen on higher notes.
Maybe it could just be the act of pulling out the mouthpiece and disengaging from the nodes of the standing wave in the horn.
I'm not too worried about it and don't plan to change anything. Still, I find it interesting. Oh and by the way, if I pull the horn off my face while attempting to continue the sound, the buzz simply stops. I know there are different opinions on this but I'm siding with the camp that says the buzz should stop.
If you try this experiment, I'd be curious to hear about your results in the comments section.