Great catch.
Absolutely and completely: here the "T" should be held, and should not be pronounced with a sharp burst of air。Or in Chinese: "T" 在两元音之间失去爆破,就是说只作它的发音动作,而不发出它的音来,快速滑入下一个音。
let or best: you're absolutely right, exp. for the word "best"in this reading。
I couldn't wait having your comments on the subtle differences of pronounciation points.