In a blank autocomplete field, if you hit the spacebar, you immediatly get an error dialog box:

An HTTP error 403 occured.
http:///autocomplete_widgets/flexifield_gym/field_ff_gym_name

After you dismiss the box, everything functions as normal, except that the autocomplete options are not presented.
As you can see, I was using autocomlete widgets inside a flexifield, I don't know whether or not that's required to replicate.

Another class of bad input that causes the same problem, is any string that contains \