Check all grout lines at countertops and tub and shower surrounds to make sure they are sealed and are not cracked. Re-grout where necessary. It is very common for new construction builders to not apply grout sealer over grout lines, a recipe for cracked grout lines and water intrusion down the road.
Use the test and re-set button to test your GFCI outlets. Better yet, for usually less than $10 you can buy a GFCI tester and make sure all GFCI's in your home, including those that do not have test and re-set buttons, work properly. Any outlets that do not re-set should be replaced. You are supposed to trip and re-set all GFCI's monthly.
Run the sinks with the sink stoppers seated so the sink fills. Let it go until it is flowing water through the overflow drain. Open the sink cabinet and turn on a flashlight to check for leaks. Then let the stopper come up and watch for leaks and for proper whirlpool action as the water drains. If leaks are found, repair them. If the sink will not drain properly, use liquid drain cleaner to open them.
Check bathtub for whirlpool drain action. If the tub will not drain properly, use liquid drain cleaner to open the drain. Periodically remove the drain strainer and remove the hair that builds up below it in the mouth of the drain line.
Run all shower heads and look for leaks at the shower head threads. If there are any, unscrew the shower head and put plumber's tape on it and put the shower head on again securely.
Check your furnace filters. Your furnace will run a lot more this time of year. The more it runs, the more air that gets filtered, resulting in filters that need cleaned or replaced more often.
If you have permanent filters, made of metal, flush them out at an outside hose bib or in the shower. Then let them dry thoroughly before reinstalling them.
If you have disposable filters, just write down the three numbers on the filter frame, then take those numbers to the hardware store. The number stand for the length, width, and depth of the filter. For example: 24 x 12 x ½".
If you didn't drain your outside hose bibs, make sure to buy covers for them. Hose bibs that have water present can freeze during very cold nights if they aren't covered, resulting in burst pipes and VERY expensive repairs.