Bad flashing is the quickest way too leaky ceilings, wet insulation, mold, and expensive repairs. It is what protects the inside of your home around the chimney, and is located where your roof and chimney meet.
It is often one of the most problematic areas of the chimney, and often not installed correctly, or sealed with tar or caulk that is not designed for sealing the flashing. One small exposed area left unattended can cause major damage. i.e. leaks in the ceiling, wet insulation, rotted roof boards, damage to shingles, etc.
Tar and caulk is just a temporary bandaid and will not last long. During your next chimney or roof inspection, remind them to inspect the flashing as well, to make sure it is watertight.
Often the back of the chimney flashing is not sloped properly to drain water. Also, leaves, debris, raccoon, or squirrel droppings block the ability for it to drain causing it to hold moisture.
Starting in 2012 IBC (International Building Code) made it a code that chimneys over 30 inches wide must have a cricket installed perpendicular to the slope of the roof. If you have an older home your roof may not have a cricket.
Chimneys that are properly flashed will have the top of the metal or lead embedded in the mortar joints of the chimney, also it will be secured tight to the brickwork, have all seams properly sealed, and will be terminated under the shingles overlap.