Very good Bea.
A couple of things to work on: On "Oh, Susanna" you play the base note too early in some places. The counting is quite difficult in this piece, so I recommend you try to sing the melody line, and then nod your head (or stamp your feet) where the base not should be. Then when you get the feel for where the base notes go, it is easier to get the thumb to play the base notes at the right moment (where you nod:-)
On "Que ne..." you damp the first A base at the pause, but the next E you don't damp, but more important is that in measure 3 (4 if you count the first) you should try to damp the D and the E with your thumb right after the next base note is played.
I'm sure this tip goes for some of the earlier recordings in this lesson (I've not reviewed them now)...
Measure 3(/4) base line should go like this: C, D (lift 3 finger to damp C), E (damp D with thumb and prepare for A), A (damp E with your thumb)
In order to make all of this happen without disturbing the rhythm it is essential to go slow enough. I recommend to practice this measure a bit even if you don't manage to do it when you play the whole piece, as the thumb-damping-technique is very important to master, and the * marking will eventually not be marked in the scores. My experience (I did D01/D02 the year before last) is that now my thumb often damp the last played open string base note automagically