My Fiance and I are having a similiar problem. WiFi seems to be fine, but 4g/data is screwed up. I got the S3 when it first came out, and it ran GREAT. These problems have popped up in the last update or two from Tmobile. It is really annoying.
You guys are scaring me to death I just bought one off ebay and it will be here Monday I had the S3 before on sprint and got great reception everywhere but that's sprint!!! Isn't the S3 4G/LTE that's what the spec page says