I have Cateye's on all my bikes and those also have a second or two delay to update the display. Once in a while I will look down and see a speed that I know is way off from what I am riding at and then a moment later it will update to what it should be. New battery certainly won't hurt and is cheap.

I have made the habit of putting new batteries in my computers at the beginning of the year. That way I know they won't die on me mid year, and I start each one off with a mileage reset for the new year. Probably overkill, as the batteries should last several years minimum, but they are cheap.