If I am checking for myself, before the inspection, I like to tap on things, like walls and railings, that have a fresh coat of paint. A lot of problems are hidden this way and I don't want any surprises once I move in.
If its an older house I tend to look for any possible problems with damp, and electrics. Also the state of the window frames and the heaters or boilers. Generally, anything that could be expensive to fix.
I like to get in depth and look at everything from the foundation up, but I also like to look through county records regarding any improvements or service that has been done at the house.
when purchasing a house, first thing i would check for is the floor. the walls comes next, they should be well painted. i like big rooms and a big comfort room with a bath tub. i also prefer a big yard at the front.