At the risk of being a killjoy: the episode is factually correct. In 1987, there was no GSM service in the US. In fact there was no GSM service
at all. The standard was still on drafting table, and the first GSM network wasn't launched until 1991, in Finland. At this point, pretty much everything was analog, and the iPhone, Treos, blackberries.. none of that stuff would have worked.
And in 1997, GSM service existed in the US, but only in 10 or so major cities, each run by much smaller PCS companies. AT&T hadn't launched their implementation yet. There was also no EDGE data.