36k miles in 1 year? As Bort mentioned, they might be hard miles. On the other hand, Those 36k could also have been a LOT of freeway cruising (that isn't nearly as hard on the car's parts) given that it's from Kansas and you have to drive for hours to get anywhere from there.
I completely agree with Bort on with having a trustworthy mechanic put it on a lift, most mechanic shops around here charge $100 for the service and will provide a printed list of items after evaluating the car. That $100 will save you from buying a lemon if there's a serious issue under the hood (like a flood damage that's not listed on the Carfax).
Don't put any faith in the Carfax report. Only participating mechanics report work to Carfax. Any number of things can happen that will not show up on that report if the mechanic who fixes it doesn't share the data, or if even a participating mechanic gets the VIN wrong when reporting it.
Check the website
http://www.safercar.gov to see if there are any general recall issues with the model you're looking to buy. If you have the VIN, run it through that website to see if the rental company had things fixed on recall, or if it's going to need to spend time in the shop. Rental companies are really bad about NOT fixing recall items on the cars they have since they turn them over so fast.
Expect that you'll need to buy a set of tires soon. The rental companies don't rotate tires like they should. Assuming the car still has the original tires, they are likely the most abused part of the car.
Go on an Altima owner's forum, check out what everyone is complaining about for the models 2-3 years older than the one you're looking at. Then check auto blogs and magazines to see if Nissan has fixed the main issues that come up on the forum for (or prior to) the model year you're looking at. Check to see if the issues are specific to an engine or transmission type.
For example - Ford Focus owners are now complaining everywhere about the auto transmission for recently sold vehicles (past 3-4 years). Ford still hasn't fixed that issue. It has to do with removing the transmission from the car to replace a wear part every 20-40k miles, not covered by warranty since it's a 'wear item'.
It's also worth checking JD Power's and Consumer Reports ratings for that model/year too. If you don't know someone who subscribes to CR, you should be able to find it at your local library.
I haven't heard anything bad about Altimas in general, but these are the steps I'd take when buying just about any used car. I skipped the mechanic part when I bought my current used car, but only because I was buying it from my dad and I
know the car's repair history.
Overall, the rep for the Altima is now about on par with the Corolla family that Bloke mentioned.
They're plentiful now so parts are not expensive and can be found at the local parts store almost anywhere in the US.