Chimney photos: P 138, P 145, P 147, P 205, P 218, P 219
Use your binoculars to view the chimney. The base may be built in the middle of the house. In this situation you'll only see the portion of the stack that protrudes through the attic and roof. Some homes will have the chimney built along the side of the exterior. This type of installation will have a chimney foundation that is separate from that of the house. As with the house foundation, the footing must be below the frost line in cold climate areas. Check to make sure that the chimney isn't leaning. A leaning condition is a serious problem and it would have to be repaired.
Make sure the mortar joints are in good condition and don't need repointing. You may see the terra-cotta tile flue linings at the top of the chimney. Make sure they aren't cracked or broken. Each flue pipe in the chimney should vent out of a separate stack. When you see two flue pipes, one is for the fireplace and the other is for the heating system exhaust. The top of the chimney stack should be high enough above the roof line to prevent downdrafts. Downdrafts are caused by air currents over the roofline pushing cold air down the chimney flue pipe. This will prevent the exhaust gases from properly venting out of the house.
If there's an antenna attached to the chimney or the roof, make sure it's caulked. Caulking is needed so that there won't be any openings to allow water into the house. If there's cable TV in the house and the antenna is no longer in use, then the antenna should be removed. Antennas add stress to the roof and chimney when they move around in the wind. They can create water leaks.
There should be a weather cover about one foot above the top of the chimney stack to prevent water from entering the flue. There should be a screen over the top of the flue stack to prevent animals, such as raccoons, squirrels and birds, from entering the flue. I once did an inspection on a vacant house and when I looked up the interior of the fireplace flue, a raccoon was sitting there. This raccoon took one look at me and ran like hell out of the top of the chimney. (I guess that doesn't say much for my looks, especially if that was a female raccoon!) By the way, don't go near any raccoons. They're beautiful looking animals but they carry all sorts of diseases, including rabies. You also want to be careful if you're allergic to bee stings or if there are ticks that carry lime disease in your area. Sometimes while you're inspecting the exterior of a house, you'll have to move through the shrubs to get a closer view of the foundation area. By doing this, you can get stung.
Some chimneys are made of metal piping. Check these chimneys for any rust. Often on condominiums you'll find that metal chimneys are covered with a finished wood siding to match the exterior wall siding. You'll be limited in what you can see with this type of installation. Just do the best you can.