This is happening to me too, and is absolutely frustrating. The crash is random and seemingly non-reproducible, so when it crashes, it takes down all the work I was doing.
Mission Control/Show Desktop seems to trigger the bug, but it's not an exclusive trigger. It also happened playing youtube videos or moving windows around.
By the way, on my displaylink-driven monitor I have no Apple logo (the rest of the menu bar looks as it should, though), and no miniatures on Mission Control. Video is super choppy, and some windows turn black randomly. I have to move them to the MBA's monitor and back again to refresh them.
Overall I am not happy with the performance of the Displaylink and I'd like somebody to fix the issues once and for all. This is a product I can't definitely recommend. The annoyances are one thing, but the random crashes make it almost unusable.
Sorry for the criticism but this is unacceptable.
PS: I'm running 10.9.2 on 2013 MBA
Edit: my latest crash log
https://www.dropbox.com/s/jfnr37xd61...ndowserver.txt