On the newer electronically controlled automatics, I don't think manually shifting them does very much. The computer still controls the actuation of the gear change and has some ability to protect itself. I think the clutch packs that engage the gear may wear out a little quicker if done frequently, but the actual gears and torque converter don't care. I go from D3 to D frequently to get more compression braking form the engine going down steep hills or to prevent upshifts to 4th/5th in slow city driving.

Manual transmissions get btter mileage because as mentioned, a manual clutch provides more direct power transmission, a manual is typically 50-80lbs lighter, and in some cases the gear ratios a more favorable. However the newest generation of 5, 6, and evne newer 7 and 8 speed automatics (Mercedes & Lexus) actually get equal or sometimes better mileage and in some cases accelerate faster.