Not that I want to contribute to the flame war here, but I am experiencing similar problems as the OP. I wanted to take my phone back to Sprint to have it swapped out, because on top of major signal issues, I have extremely glaring OLED defects on my screen that I see at night. I already swapped it once, and saw no improvement on signal OR OLED problems.
Here are my issues:
- Much worse cellular signal in the same places I used my Evos... Real-world experience with dropped calls, straight-to-voicemail, and texts/mms not sent or received. I miss about 50% of my calls. Infuriating.
- BLUETOOTH is garbage on this phone. I have a Beacon BT audio cube that works from nearly 200ft on my Asus Transformer TF301, and my Evo 3D, yet, on my S3, I get audio chopping out at FIVE FEET. If I put my hand on the back the phone in a certain way, I can cause the signal to drop out entirely.
- WiFi is pretty much a joke, when compared to any other device, ever produced. The Eye-Fi SD card in my camera has literally TWICE the range. I kid you not. A WiFi antenna crammed into an SD card performs better than my $600 cell phone? Thanks Samsung

- I also have MAJOR issues handing off between EV-DO and LTE. I don't live in a market with LTE yet, but I visit them quite often. Typically when I hit an area with LTE, my phone just loses all internet connection. Not cool. I have tried various modems, and PRLs, with no luck.
- GPS antenna is WEAKER than my Evo 4G and Evo 3D. It locks fairly quickly when outdoors, however. On-par with my HTC devices.
I then got to talking to several of my friends and family, and I found out the problems weren't just with me---and they weren't limited to just the S3. I have friends with these phones that have eerily-similar problems:
Samsung Epic 4G
Samsung Galaxy S2 (Sprint)
Samsung Nexus S 4G (Sprint)
Samsung Galaxy S3 (Multiple carriers)
Samsung Galaxy Nexus (Multiple carriers)
I have seen these phones deliver lackluster signal strength, _especially_ with WiFi--in person. I have now come to the conclusion that Samsung radios are inferior to the competition. Perhaps this is how they make their phones slimmer--I do not know. Coming from the older HTC Evo line of phones, I can say I am seriously disappointed with ALL radio performance in this S3, and all other Samsung Android phones I have ever touched. Sounds harsh, but I am basing this off of actually using the devices.
I am considering going into the store with a few bluetooth accessories and trying all the phones on display. I might have to switch to the HTC Evo LTE 4G. I used to be able to walk over 250-300ft away, in a giant datacenter, from my HTC Evo 3D and still get flawless stereo sound from my BbD headphones. Now I can't go over 20-30ft before losing signal completely. Static and cut-outs start at 5ft or less sometimes.
blah.