Lampshades: Run a lint roller over the inner and outer surfaces, then blow dust from seams with a hair dryer or a can of compressed air.
Litter box: Every few weeks, place the whole kit and caboodle inside a garbage bag and shake to dump out every bit of old litter. To clean the box, cut down on the ick factor by wearing rubber gloves and scrubbing with disposable heavy-duty textured wipes (Litter Box Wipes, $10, naturesbestsolution.com for info). Never use bleach. It can react with the ammonia that naturally occurs in urine and potentially create toxic fumes.