Unlike many popular automatic transmissions of the 1950-1980s, on modern systems, there is no need to adjust kickdown cables, or clean mechanical governors (which prevent engine overspeeding) and to set brake bands periodically.
However, modern automatics rely still on the correct quantity of specific fluids to maintain reliability. Always follow level check advice carefully, because it is easy to make mistakes. Take extra care to ensure that you pour new fluid through the correct aperture and do not dismantle part of the gearbox unintentionally, by undoing an external bolt instead of a plug.
The oil should be clean. Dark-coloured fluid indicates a major internal problem, due possibly to overheating, or deterioration of the clutch friction plates. While many transmissions are described by the car manufacturers as being sealed for life, it is accepted that periodic fluid changes are beneficial on an older vehicle.
Pay attention on a road-test, too. Any jerks, clunks, harsh changes, or a sudden engine speed rise between gear changes (known as ‘flaring’) will need investigating. It is possible that such issues might not illuminate a warning lamp on the instrument panel.