sustaining air and sound, and pulling slides for intonation

Today I had a lesson with Larry Johnson. I played a number of excerpts, and he noticed two patterns in my playing.

I tend to drop the blow before I articulate notes, or toward the end of long notes, when I should be sustaining or increasing the air. In the Beethoven 3 2nd horn excerpt, I wasn't blowing through the first dotted-half-note In Shostakovich 5, the low tutti, I need to blow through the articulations, sustaining all the way through the phrase. And in the high, quiet solo, I should use subtle crescendi the beat before moving to give the phrase direction, as well as set up the slur.

The second pattern is that I don't always consider the key I'm in and treat the 3rds accordingly. He encouraged me to pull the slide that's used for the 3rd, if possible, or find fingerings that get everything in tune. It really helped, for example, in Gliere to use 3rd valve on the F side for the E at the beginning of the lyrical tune. Also, pulling T1 in Fidelio, or T2 in Brahms 1 call.