I've seen a lot of complaints about the Band 2 being inaccurate in a few ways, such as undercounting steps and flights of stairs. I've noticed the same and I think the heart rate is also off. Some people say it is more accurate if you wear it with the display on the outside of your wrist with the buttons facing up the arm, but I have no idea if that's true. I've been wearing it on the inside and flipped it a little while ago so I'll see if it makes any difference.
Update:
I took a walk on a treadmill to do some comparisons. The heart rate monitor seemed to work better with the display on the outside. It was somewhat in agreement with the treadmill's heart monitor, although they differed up to 10BPM or so on occasion. I don't know which is more accurate, but maybe it's a sampling thing. I guess you can't really expect scientific accuracy out of something like this. I think you need a chest strap if you want the best accuracy but I'm not that hard core.
The step count and distance on the Band were wildly off though, and I believe it's due to its reliance on arm movement. If I held on to the treadmill hand bars where the heart monitor sensors are then the Band counted nothing, zero steps, zero distance, for that time. I walked 1.5 miles (according to the treadmill), and the band measured 1.06 miles. I also had a Fitbit Zip clipped to my pants pocket which counted 3216 steps, the Band counted 2054. Separately, the Band shows I climbed 2 flights of stairs today which is well short of reality.
For the day, the Fitbit shows 6373 steps and 3.09 miles walked, the Band 3620 steps and 1.88 miles walked. Based on what the treadmill says I'd have to say the Band is not at all accurate and is going back to the store.