some of Apple's iPods did have a battery issue, but this is also due to the fact that people have no idea how to care for a rechargeable battery (So many people moan that things like their cell phone has crap battery life because they're too inept to use the battery correctly) but this has been addressed in newer models and therefore shouldn't be a problem with the iPod Mini.
These so called battery problems hardly affected a large percentile anyway, plus regardless of the "problem" iPod still takes 3 positions (including first) in the top 5 selling mp3 players worldwide at the moment.
I'm not sticking up for apple, this is just what I've heard, I do not own an iPod myself and therefore can only judge from the opinions of others, it is funny though how a few people can bad mouth something, and the thousands and thousands of happy customers stand for nothing.