Friend of mine has a white MB that developed a battery problem when (naturally) it was 1 year and 2 days old. No, she didn't have AppleCare.
No bulge that I could detect, but the battery just suddenly stopped being "seen" by the computer. It started with the computer seeing but refusing to charge the battery, then progressed to the computer not seeing it at all. Now, when the battery is inserted and the computer is started, the front panel light blinks--two blinks, pause, three blinks, pause, over and over. Removing the battery lets the computer start normally.
Sadly, since it wasn't physically bulging, and was two days out of warranty when she brought it in, Apple refused to replace it.