For several days in, this post is surprisingly light on the "issues." I haven't had an issue with registering taps on the browser, so I don't know if this is a hardware or software issue.
I have never been a fan of motion controls or gestures because I have always found these to be flaky in real world use - that's why I am glad that Android as an OS mostly depends on buttons and menu options. S-Voice is terrible, but the Google voice commands are still there with the little microphone right next to the search bar on the home screen. The Samsung keyboard with its faux Swype T9 really sucks, so I downloaded the Swype beta, which is a huge improvement. The screen dimming is the one thing that is legitimately annoying for which there is no easy fix.
The battery life has been awesome for me: on Saturday it lasted from 8 am to past midnight with 15% left even though I have multiple widgets, live wallpaper, push e-mail with syncing from multiple accounts, and I was recording 1080p video with the screen on for quite a while. The biggest source of battery drain for me on my old phone was weak cellular/data signal, but the radios are much better on the S3. However, if you are in an area with very weak Sprint service, the battery will probably still drain quickly. With my old phone, I just learned the particular rooms and buildings at work where I had incredibly weak signal and toggled airplane mode as I went in and out. This may not be a reasonable solution to your problems, just my experience.