This is by far the best advice. This allows a professional to inspect all of the components of your system for the season and possibly prevent an issue before it becomes a more serious problem. After all, nothing ever breaks down when it's convenient! It is recommended to have a system inspected twice a year...once in the fall or winter (furnace) and again in the spring or summer (A/C). Think of it like an oil change on your car....although you may not be experiencing an issue when you hit 6,000 miles, you don't wait for your car to break down to realize there's not enough oil in the engine.
Checking your air filter each month will ensure the proper air flow is getting through to your system. It will also make sure your filter can continue to remove any air particulates from the air as your system operates. In addition, a clogged air filter can place unnecessary stress on your heating and cooling system, causing additional wear and tear and higher energy bills.
Most thermostats have backup batteries and although the batteries aren't always in use, they can certainly cause issues to the overall operation of your system. Ensure there is no visible corrosion or expired batteries. If you have any heating and cooling system issues, replace the batteries in your thermostat with fresh, new batteries. This will ensure your system isn't reading any false signals as a result of bad backup batteries.
A bypass humidifier will have a damper that will need to be turned to winter/summer depending on the season....make sure the switch is set in the proper place.It is recommended to change the humidifier pad annually as well. This will ensure the humidifier is operating at it's peak capacity. Also, if you are experiencing condensation or ice on your windows during extreme weather, try turning your humidifier to 25% on your humidistat (usually there is a dial or a digital screen located on the side of the furnace duct work).