Haven't watched the presentation yet, but I believe the GCN might have been the first console to come standard with "analog" shoulder buttons (dutifully demonstrated by its use in Mario Sunshine to control the spraying power of the backpack).
EDIT: Oh also, the Wavebird controller was the first wireless first-party controller.
The PS2 beat the GCN to market by a year and had not only analogue shoulder buttons, but analogue face buttons too. Even the d-pad was analogue -- everything except Start/Select/L3/R3. It wasn't very widely used, and causes some problems in porting games that relied on analogue face buttons (like Metal Gear Solid 2 and 3).
EDIT: Oh also, the Wavebird controller was the first wireless first-party controller.