Two comments:
1. Yes, if you're playing a song and you hit the home button or sleep button, the song continues to play. Suggestion: you can tell if a song is playing by pulling out your headphones and listening on the speakers.
2. I too am having battery issues and considering stopping by Apple store tomorrow. My computer went to sleep last night, but I still left this morning with ~90% charge. But with ~1 hr of usage (video, email, phone) + 10 hrs standby, I had less than 10% when I got home. I'm wondering if this is a calibration issue with the battery meter -- that I haven't been able to fully charge it yet so, like on our laptops, it doesn't have accurate power management, or if my battery is defective. I'm doing a full charge now and will report back.
I wish people who didn't have battery issues would glance at this thread and report what we _should_ be seeing 🙂