"Dear Cotswold Port Co, why do some bottles of Port have what appear to be splashes of white paint on them?"
Some ports have a splash of white paint on the bottle. This white mark is also called a splash is painted (splashed) on the uppermost side of the bottle and is there show which way up it was cellared. You too should then store your Port with the splash of white paint uppermost. This allows the sediment to settle uniformly in one place. Then when decanting keep this mark uppermost to minimise the amount of sediment poured.