Disclaimer: I have never purchased a house, but I've been with family while they've looked, and have heard about all the stuff they wish they had checked!
I have to say, I strongly advise checking that all windows work and are properly put in and sealed. My sister moved into a brand new house in AZ, and it was inspected, and later they discovered that the upstairs bedroom window was no only hung crookedly, but also had about a centimeter gap under the window where it hadn't been sealed properly to the wall and you could see straight through outside!
Also, make sure you get to inspect the house without the furniture in it VERY thoroughly, especially the walls. My best friend's house has walls that have most obviously been poorly patched in several areas because of water damage. Don't be afraid to push on the wall a bit if you suspect an area to be weird or soft.
Which leads us to:
Check under every sink in the house to make sure that the cabinets (if they're staying) and floor has not suffered water damage. I moved into an apartment once and didn't check for that, opened the kitchen sink undercabinet, and discovered that the whole shelf had completely rotted out due to the sink leaking. Luckily I was renting!
And finally:
Check the carpeting! My mom just rented a home and didn't notice that the previous tenants obviously damaged the carpet in the corner of one room, and replaced some of it with a poorly done and poorly matched patch. She had no idea for a week or two, because you can only tell if you stand in the room near it and look at the floor directly. It's bad for the carpet though, as it could eventually come loose and wrinkle. Don't be afraid to pull up on the pile of the carpet to see how loose it is! The last thing you want is to trip over a lump in your carpet :/
Oh yeah, one more! Be afraid of area rugs! My dad was renting a house out, and he approved them to move out and discovered later that they had hidden a huge burn in the carpet with an area rug! They also had serious damaged the hard wood floors in the bathroom, but hidden it also with a small rug over the top.
Sorry if that was a lot! Hope it helps some!