Make sure you have good ladders- a 24 foot extension, a six foot folding ladder and a little one, a two or three stepper. Most homeowners have extension ladders that I wouldn't trust- get a good one that you aren't extending all the way every time you use it. They are much more stable when extended only half or so.
I second Roy's advice on getting to know the place. Get in the crawlspace if there is one, if you have a basement look up and see where all the wiring is going. If the house was built in '39, you may have a few generations of electrical stuff going on, so make a note of the kinds of sheathing you see on the wires, which helps you to know how old it is. It will also give you an indication of how much messing around previous owners have done. Make sure your service is adequate- at least 100 amps, but 200 is best (but unlikely, given the age). Also, get to know the breakers and what they control. Know how to shut off your entire panel.
Crawl around the attic and look at all the wiring there, too. Inspections are all right, but look at the fine print and you will see they only inspect what they can see. Pull up the insulation, look at the junction boxes and make sure they are all closed. And speaking of insulation, make sure you have enough. If you can see the rafters, then just roll another layer perpendicular to them.
Inspect the eaves and the roof for proper ventilation. Most houses that age do not have good attic ventilation. It's not a deal killer because those houses are not as air tight as newer ones, but ideally you will have a way for air to move into the eaves and out the highest point of the roof. So, if your new roof had vent caps, you should also have eave venting as well.
Get to know the plumbing. That age house may have some galvanized pipe, but for the most part you should see copper supply lines. Tighten all the valves, read up on the kind you have and if you're really ambitious learn how to pull them and replace them.
You probably have cast iron waste lines. They last about 80 years and eventually you may see pitting on the outside, which indicates their end of life. Easily replaced by a plumber with PVC. How fast do your drains run? Old drain lines can be as small as 2 inches, which is pretty small, so if you are ambitious you can learn to run an auger down to the public sewer (or just call Roto Rooter). I do mine once a year. Inspect all the goose necks on your sink drains. Sometimes you will find that the chrome plated ones are in bad shape. Easy job to swap them out with PVC, requiring only a hacksaw and a pair of channel lock pliers.
Seal all the holes in the foundation. Helps keep the rodents out (although I live next to the woods and have some to accept mice in my attic as a regular nuisance). Make sure your inspection also included a termite inspection. Make sure you don't store wood next to the house and make sure that you have a few inches of space between the top of the soil and the sill plate (where the foundation meets the walls).
OK, this last one is really important- make sure you have ground fault interruption outlets in places where there is water- bathrooms, around the kitchen counters, any outdoor or garage outlets. I also pull the cover plates off of all switches and outlets that don't look original because I trust no previous home owners when it comes to electrical installations. I look for wire nuts that are too small, sharp bends in the wires or an indication that someone just jammed the stuff in as quickly as they could. Good electricians make neat installations.