They are not efficient like powerheads, water pumps, and/or protein skimmers are at creating water movement in an aquarium. All of these are much better at helping with oxygen and other gas exchanges at the water's surface.
They do not move water fast enough or in adequate volume for what a tank usually needs for good all round, vertical and horizontal, water circulation. This situation can also contribute to a low or insufficient GPH (gallon per hour) tank water turnover time.
They create a lot of salt spray, that in turn contributes to salt creep problems.
They clog up.
They wear out quickly, and usually need replacing often.
They can give off irregular air flow.
Air line hoses can get pinched or kinked, which weakens or cuts off the air flow.
Many times the air pump chosen to run air stones is inadequate, resulting in low air flow pressure.
Some air flow pressure is lost the longer the distance the air has to travel through the clear tubing from the air pump to the air stones.
The deeper the tank water, the farther the air has to be pushed downhill to reach the air stones, resulting in loss of air flow pressure.