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As I noted, the Wi-Fi problem only happens with a small percentage of phones. If you do a search on "Galaxy S III Wi-Fi problem," you'll find it in the discussion boards. I ended up taking the first phone back and getting a replacement. The second one connects to the wireless network flawlessly and Wi-Fi is fast and reliable. I don't know whether this has anything to do with it, but there was a sticker on my second phone that said "Updated" and there was no such sticker on the first one.