Look for an inspector who has considerable construction experience. How can an inspector know what is, or is not, a problem if he doesn't know how homes are built?
Look for an inspector who has proven himself competent. A contractor's license or a building inspector certification, for instance, requires considerable study and testing to achieve. In most cases the individual has had to prove his experience to achieve that license. They also require regular continuing education to make sure the holder is up to date on current information.
Look for an inspector who is certified by a national home inspector organization. Most of these organizations have certain requirements as to experience and training in order to become a member and most have certain continuing education requirements to maintain membership.
Look for an inspector who has experience inspecting homes. You probably do not want the first inspection he makes to be on the home you are planning to invest your life savings in.
Look for an inspector who not only tells you he has the experience, look for one that makes it easy for you to verify that experience. He should have easily located links on his website that allow you to confirm what he says.
Finally, take the time to talk to the inspector. Make sure that he is willing to take the time to answer your questions and you will feel comfortable working with him.