The first answer I came up with is cillia - zillions of microscopic filaments covering their surface, used for propulsion (but what are they pushing against? If it's air it must be VERY dense), to adhere to things, etc. It sounds good, but there's no evidence for it whatever, and Abbot makes a big point of how flat their lines are.
So I'm wondering... if they're genuinely one atom thick could it be some sort of quantum or electrostatic effect? In the thread on visual processes yesterday cdybedahl pointed out that there must be a lot of energy going spare if there's the omnipresent white light Abbott describes. Maybe they use some of it to move, manipulate and stick to things, etc. In fact they might use this energy for all their needs, using food only for growth and repairing wear and tear of the body etc.
What I need here is some hand waving - this is almost good enough to go in as speculation as it is, but a bit more would be nice. Or if someone has a better alternative please post a comment!