Interesting point about the one hand vs. two hand operation.
I haven't had a problem with dropping the phone, but I do use two hands to operate it except for simple things like scrolling. That's easy with one hand - at least for normal vertically scrolling websites.
It does get annoying reading Kindle books with their ridiculous sideways page turns where you have to tap the right side of the screen or drag the page sideways. I love having all my books and magazines on my phone, but hate the Kindle UI. Why can't I just scroll my books vertically like a normal website? Being right-handed, I hold the phone in my left hand, so it's a pretty awkward reach. [1]
The few close calls I've had were when I tried to get fancy and reach across the phone with my thumb to tap some button on the screen - or flip a Kindle page. Definitely see how it would be easier to drop if you're using it one-handed.
[1] This reminds me of a question I've been curious about: I've read a few times that most people hold their phone in their dominant hand (e.g. my right hand). I never understood this, since I use it more like a small pad of paper and pencil - the pad of course would be in my left hand and the pencil in my right. Naturally when I'm using the Note's stylus I do it that way, but even without the stylus I've always thought of it like a pad and pencil with my finger being the pencil. I've always assumed that people who use their phone with two hands do it this way, but I'd be interested to know whether people who operate their phones with one hand use their dominant hand or the other hand.