I've been doing some practicing since my lesson on Tuesday, and I can definitely tell one of the big things I need to learn. I can pick the notes given no beat and all the time in the world, but put even a slow beat to the notes, and I'm picking the wrong notes at the wrong time!
I think there are a few reasons for this. I have to override where my fingers naturally want to go in order to pick a note, and I don't perfectly match up a fret and string to a note on the staff. When I get bored with fast finger exercises I move on to songs where (right now) I give myself all the time in the world between notes in the tab.