What about the screen issues?
While there seems to be more reports than usual of cracked screens around here, I've not had any problems. Just keep in mind that it's large piece of glass that you're carrying around. Also, you have to remember that forums are where a lot of people go when they have problems, so the conversations in the topics you see will almost always be negatively skewed. Most users who don't have any issues don't come online all the time to start a new thread to say "I don't have any issues!"
It's definitely better than the Rezound, and in my experience, better than the stock battery of any other LTE device on Verizon except the RAZR MAXX.
Reviews are great, but how does it hold up through a month or two of use?
It holds up great. I've had no problems, and the phone still operates as smoothly as the day I received it.
Only you can really know that. But in my opinion, the phone is definitely worth its price on contract and it's definitely worth paying up to retail price for off-contract. It's a great device.
I really want this phone.
Then what are you waiting for?
I'll add a couple other quick observations about the S3 versus the Rezound (which I used to have). The screen is half an inch larger, and you can definitely tell. If you like large screens, you'll love it. And even if you don't care for a screen that larger, the minimal bezel and thinness of the device go a long way in making the screen size extremely usable. Reception was noticeably better on the Rezound in areas with weak signal for me. The S3 definitely has much better reception than the Galaxy Nexus, but it's not quite up to the level of the Rezound. Samsung just hasn't quite nailed down the radio game as well as other manufacturers have. That said, the reception on the S3 was good enough for me to give up the incredible reception of the RAZR MAXX, so it has done well in my use. Call quality on the S3 also lags behind the Rezound a bit, but it's still above average. The camera on the S3 is a little better than the camera on the Rezound, but not by much, so it's pretty much a wash there.