Tried but couldn't replicate your problem, my dropdown box lands neatly below the bottom of the box. If you're using IE, check that the zoom level is 100%, site does strange things if it's on 125% or 150%. Since it's also happening on the forum new thread page, this is the most likely cause of the problem.
In any case, the problem is likely to be in your browser, so you can test that theory by trying a different browser.
If you don't want to do that right now, just put an extra character such as * at the start of your typing, and the dropdown box won't open at all.