During the Scooby meeting in the first scene, the fabric on Buffy's shirt flips up at the shoulder, but the flip changes from right shoulder to left shoulder repeatedly.
Buffy throws a sword at a Watcher who interrupts her. In the wide-screen version, you can see that she never lets go of the sword.
Buffy says, "There's also near consensus about Columbus, you know, until someone asked the Vikings what they were up to in the 1400s and they were, like, discovering this America-shaped continent." The Vikings settled in North America around 1000.