Note whether or not the ceiling held up by the joists sags or is uneven or wavy. Also note whether that condition changes over time. Because some ceilings are built imperfectly, a sagging ceiling may not indicate damage to the joists. A ceiling that changes, though, indicates a problem.
Inspect all joists in the attic. Use a flashlight to help you see the joists clearly. Move insulation out of the way to get a good look at all sides of the joists. If your house experienced a traumatic event such as a tree fell on the roof, look for cracks and breaks in the joists.
Search for signs of rot or decay in the joists. Dry rot and wet rot are the broad names of the two most common kinds. Ceiling joists are more likely to be affected by dry rot than wet rot, unless a leak is in the roof and the joists have been wet a long time. If you find a joist that is crumbly and exhibits white, moldy looking substances on its surfaces, it has dry rot. If a joist is mushy and damp, it has wet rot.
Look down the length of the joists to see how straight they appear. Some joists are warped when they are installed. So a non-straight joist is not necessarily a concern unless its condition worsens. A non-straight joist is most likely to happen in a newer house in which the builder used joists that weren't dried properly.