The surface of the glass under the plastic film is not as smooth as other phone screens. I think this is because it is not intended to be used without a film above it.
I removed Sonys plastic film and added Orzly Tempered Glass Screen Protector (you can use any other tampered glass protector). nearly perfect for my and much more scratch resistant than with the plastic film.
History: Philips Savvy -> Trium Galaxy -> Siemens S25 -> Ericsson t68 -> Nokia 6230 -> SE w810i -> SE w890i -> iPhone 8GB -> Nokia N79 -> HTC Touch Diamond2 -> HTC Legend -> HTC Desire S -> HTC One S -> Sony Xperia Z1 Compact