The solution is simple but annoying: you need to enter the DNS server info manually for every Wifi you want to connect to. I use Google's DNS serves 8.8.8.8 and 8.8.4.4 and works like a charm. The several techs I spoke with at Apple are clearly stumped by this and unfortunately were not able to offer any helpful advice.
My iPhone did not connect successfully to my Wifi the first few days, and unbeknownst to me, used the AT&T LTE network instead. (I checked my AT&T data usage for those few days and sure enough, I found that the iPhone had used such a huge amount that I exceeded my monthly limit in just those 3 days. I was so nervous that I decided to turn off the 'cellular data' feature for fear of incurring a fortune in data usage charges)
I also had trouble connecting to my office Wifi, Starbuck's AT&T hotspot, and Comcast's hotspot at 10th and Mission. The problem went away when I entered Google's DNS server info in all four cases.
I will keep manually changing the DNS servers on my beautiful iPhone 5 until I get a new replacement unit.