if auto complete mode is on, it should show the list without forcing the user to click on the arrow.  maybe this is optional, but this is how i have my version built.

also, the drop down list should show if the user presses the down arrow button rather than force them to move their hand to the mouse to click the down arrow key.  that probably doesn't have anything to do with autocomplete mode, but i've done a lot of UI work in my version and i implemented it that way.