Well, you're right that they bark at everything, but one thing I've learned is that they have a few different barks. One is more of a soft, drawn out, high pitched squeal that I've only heard them use when they spot an airborne predator, like a hawk or an owl. There's another that they use for a ground threat, and it's more of a short mid range squeal. The one I pay attention to is the bark they use when they're annoyed. It starts as a short chattering bark and changes to a sort of short, lower pitched bark. Sounds sort of like they're saying "chuck".

I owe an Arkansas squirrel a note of thanks, by the way. The buck I arrowed on opening day in Arkansas had surprised a squirrel about 80-90 yards out. I heard the commotion and glanced over in time to see the squirrel scamper across the leaves and up a tree. I looked where he had scampered from and that's when I saw the 10 point that I ended up getting. I might have gotten him anyway, but the squirrel definitely let me get in position while the deer was a good ways off.