This is actually a bug caused by the Google Desktop software. Unfortunately, I think the only way to solve it is to remove and recreate all of the edit objects in your Gadget. If you remove and recreate within the same instance of script execution (aka, without a delay from something like setTimeout), then the edit objects will be recreated before the Gadget is repainted and therefore there is no need to worry about any resulting flicker. You should do this to all but the clicked edit object whenever any edit object is clicked.

At least they didn't tell you that you need to set the focus to certain edit objects in response to keyboard shortcuts. Trust me, that issue is much harder to fix...