We recently purchased a new home, barely surviving the selling of the old, buying of the new home experience. It had been almost ten years since we'd bought our last home, which was pristinely clean, only a few years old, and had no issues when we purchased it. Our new home, however, came with a few things that needed taken care of right away. Remember: "Broom Clean" has a broad meaning! So if you have just bought a new home, add these items to your to-do list and try to complete them as soon as you can (in between unpacking!)
Change the filters - You know exactly when you changed the filters in your old home, but you don't necessarily know when the sellers last changed them in the home you just bought. Not everyone writes a date on the filter, so err on the side of caution and take note of the sizes and/or models of filters for your furnace and refrigerator, if you have one. Save money and buy the contractor packs at a home improvement store. The AC man who serviced our heat pump suggested middle of the road furnace filters with pleats. Nothing too tightly woven (avoid the allergy filters, he said) because it makes your unit work harder to draw air through the cold air returns. Depending on your SEER, it can be far too much for your furnace/heat pump to handle.
Change the batteries in every smoke detector - Change them all for the same reason that you are changing the filters on your furnace and fridge. While this may have been tested during a home inspection, you don't know when the batteries were last changed. All they likely test is if they work or not when the button is pressed or if they come on for smoke. Not everyone observes the rule of changing them every six months (coinciding with the spring forward/fall back schedule). Your detectors may be hard wired, but in case of a power outage, you want to be sure they work (especially since that would be when you might be using candles for light) when you need them most.
Change the setting on your hot water tank - Your first shower might be a scalding one if you forget to at least check the setting of the hot water tank. Tanks set to higher temps will use more energy to heat and keep water at the higher temp. If you have small children, you definitely want to make sure your hot water tank is set at a temp that won't scald them. The DOE recommends setting at 120 Degrees Fahrenheit.
Check your dryer vents and fridge coils - Over time, your dryer can build up some lint balls, so be sure to check your new dryer for a build up of lint. This may require a screw driver to remove the lint screen casing to see below, but it is well-worth your time to ensure it's cleaned. Be sure to clean the duct (including the outside vent) as well. Can't get your vacuum hose in there? Try a Lint Lizard. Don't forget the screen. If you run it under water and water beads, gently clean with an old toothbrush and mild soap until water runs clear through. While you're at it, check under your fridge, too. If they had pets or just never thought to clean under, your coils could be harboring a herd of dustbunnies. Clogged coils will cost you money because clogged coils prevent air flow, which keeps your fridge running efficiently. Have hardwoods? Another reason to clean under is listed under this Real Simple list of dirty jobs.
Check your washing machine for goo - Does your washer smell funny? Chances are the previous owner didn't clean it very often. This is especially important if you have a front loader. Many times, the seals start to mildew. Review your owner's manual and initiate the clean cycle if your model has that option. In addition, gently pull out the drawer where detergent and bleach are added. This drawer, plus the inside walls, might need a good, thorough scrubbing. Trust me when I say it can get pretty gnarly in there if a previous owner does not keep it clean. Same goes for the dishwasher, get some Affresh or Dishwasher Magic and make sure your appliance is squeaky clean and free of build up. Again, you have no idea if/when this was last done by a previous owner.
Vacuum out vents or have them professionally cleaned - Your carpets aren't the only thing that is dirtier than a pig rolling in mud! Pull the vent covers and carefully vacuum up dirt and debris or pay a company to professionally clean your furnace's duct work, including vents. A clean furnace is an efficient furnace.