My battery was lasting less than a day with very minimal use. It was replace the battery or leave it plugged in for use, so I gambled the money for a battery replacement, in spite of the predicted difficulty. My previous repair of an iPod Mini was successful, but the Gen 3 is less repair friendly.
Repair went as described in the instructions. I failed to adequately protect the foil-thin connection to the touch screen during the battery extraction and it tore half-way. After completing the repair, the iPod worked, except for the touch screen.
Consider getting a 90 degree angled part that the body and touch screen can be taped or affixed to while replacing the battery. Laying the screen down flat creates an overly delicate situation and the manipulations required to remove the display and battery tend to generate twisting and movement of the body - damaging the touch screen connective foil.