I recall having a similar issue with autocomplete and zIndex, and had to fix it by specifying the appendTo option: $(selector).autocomplete({appendTo: "#copy_dialog"})
This is also useful if you have an autocomplete inside a positioned element. The specific problem I had was an autocomplete inside a fixed position element that stayed in place while the main body scrolled. The autocomplete was displaying correctly but then scrolled with the body rather than staying fixed.