The two main questions of any hypothetical Gore administration are if he wins without the Florida Incident, and whether or not you want to butterfly 9/11 at the same time. Given than nobody else is, I'll cover a scenario in which neither of these happen, no matter how unlikely it is.
As 9/11 was for good or ill the defining point which marked the beginning of the 21st Century culturally, it is rather difficult to picture an alternate Noughties without it slipping into a more extreme '90s, at least in America, as while there isn't as big an insistence on being a Proud American Patriot Who Supports The Troops (TM), the inherent social conservatism and consumerist conformity behind Suburbia is likely to continue however long you want to delay the subprime mortgage crisis (which will hit, and will be seen as something akin to 9/11 in terms of its destruction of the comfortable fantasy that permeated the era). On this front, expect a lot more in the way of McMansions, Soccer Moms, and the Helen Lovejoy mindset (remember, Columbine and the resultant moral panic still happened), but without the sense of lost innocence and the deification of the military that permeated in post-9/11 media. To this end, I expect the 2000s media landscape to be a sterilised continuation of the 1990's (doubly so if the Nipplegate debacle still happens), with the dark and edgy escapism of OTL 2000s media possibly being delayed until the Millennials fully come of age in a repeat of the counterculture movement, albeit without the backdrop of the War On Terror, and without the convenient scapegoat that Terrorists pose.
The second issue is equally monumental than the first, as the bitter divisiveness of the 2000 election, and the Florida recount effectively created the Red America/Blue America divide that defines American politics as it is today. Therefore, I believe that lacking that divisiveness, and as a direct result of the aforementioned Suburbian Consensus, coupled with the New Democrats effectively proving themselves the only electable version of it, and the partial electoral rejection of Gingrich-style obstructionism by way of two successive momentum-sapping losses forcing the Republicans to shift back to more moderate rhetoric, the 2000s politically becomes a choice of two flavours of Neoliberalism. This situation is reflected worldwide as New Labour and the Third Way becomes the defining "leftist" ideology for the duration of the pre-Recession era. This results in a noticeable lack in political polarisation relative to OTL, and a reduced geographical loyalty outside the South that could even continue to exist post-Recession.
My final, (and most realistic) prediction in this scenario is that Beltran doesn't get caught looking, and the Mets win it all in '06.
