Remove tablecloths from unattended tables. New kittens will be especially curious about what's up there on the table and will try to use the tablecloth to climb up. The result could be broken china and crystal and an emergency trip to the vet.
Unplug dangling cords. Some cats like to chew on cords. Until you know for a fact that your cat isn't one of them, it's best not to risk electric shock. Also, be alert to potential fire hazards -- lamps can tip over while you are out of the room, causing the shade to ignite and start a fire.
Cover garbage-disposal switches. Natural climbers, cats usually find their way to the kitchen sink sooner or later. Many have been known to play with electric switches such as the one for a garbage disposal. Special covers are available at hardware stores to help avoid disaster.
Keep drapery cords out of reach. It's a good idea to use childproofing devices to wind up dangling cords -- cats can strangle themselves by catching their necks in the loops.
Close the dryer door. Cats love to explore, especially dark, quiet places. Always check inside large appliances before closing their doors to make sure your cat is not inside.
Make sure your screen door has a securing latch. Cats are safe indoors; they are not safe outdoors. Don't run the risk that your cat could slip out unnoticed.
Pack away precious breakables. Cats in a new home will explore. They will jump on tables, cabinets, sideboards, and bookshelves to investigate their strange domain, and they may accidentally knock over or break fragile items and knickknacks.
Cover your furniture. If you don't want cat hair on your upholstery, put an old sheet on your most enticing sofas and chairs. That way your cat can enjoy the furniture along with you without shedding fur all over it. Simply remove the sheet when guests arrive.