The main thing you should be looking for are signs of water damage. Is any wood warped or water stained? Are there any wood surfaces that are cracked or sagging? If the answer to either of these is "yes", you should contact a roofing/attic specialist immediately.
Water seepage is akin to slow acting poison for a home's structure. Pay special attention to areas around chimneys, roof vents, and sky lights for signs of water damage as they are often quite vulnerable. Proper ventilation is also key in an attic. If there are any roof vents, blockages caused by nests or leaves are common. Make sure to clear these out by hand.
Furthermore, make sure that all of the pipes and ductwork that run through the attic are properly connected and are correctly venting to the outside. If you have an attic fan, test that it's functioning properly.