Let's start with the roof: do you see any missing or damaged shingles? How about metal flashing around the chimneys? Is that still intact? If you have any roofing issues you can see, let me know. I have plenty of roofing contractors I can refer you to.
And now the exterior. What does the siding look like? Do you see any bubbling paint or gaps in the siding? How about any mud tubes? (these are an indication of termites). If it's wood, push it with your finger. Does it feel soft? Any issues you see with your siding, write it down and make a plan to fix it over the next few months.
Now look at your foundation. Do you see any cracks? A few hairline cracks are normal, but make a note of them and check them in November to make sure their size hasn't changed.
Let's look in your attic. Do you see any areas that look wet? How does it smell? It should be dry and have no odor.
Additionally, check under your sinks and around your toilets and showers. Do you see any indication of water leaks? Any moisture? Check around the tubs and sinks to make sure the gaps are caulked.
Finally, check the basement: this should be the location of most of your systems. Can you see your hot water heater? Your plumbing drain lines? Your plumbing supply lines? Look them over for any leaks. Change the filter in your furnace. Check and see if your furnace needs to be serviced (ideally, you should service your furnace every year).
As always, I'm here to help with any advice or recommendations you need for contractors for a particular problem. I want to make sure your biggest asset stays in good working order. Feel free to reach out to me if you need a referral.