When Xander and Buffy exit the sewer at the transformer station, and the vampire in pursuit grabs Buffy's ankle, Xander initially grabs Buffy's bottom to pull her out of the enemy's grasp. In the next cut though, his arms are folded chastely across her tummy.
When The Master performs the ritual for his vessel to begin The Harvest, he says "my soul, is your soul." It transpires later that vampires do not have souls, which is the basis for Angel's character background and subsequent events in season 2.
When Harmony asks Cordelia during computer class if they are going to the Bronze that night Cordelia responds that they are because it is Friday and there is "no cover". Later on, however, when everyone is at the Bronze, the doorman can be seen counting money outside as Darla and the rest of the vampires arrive. If there was no cover why is he counting so much money?
When Xander finds Buffy and tells her he followed her because he couldn't just sit home and do nothing, he wouldn't have been home at all. Minutes before this, Buffy leaves Xander, Giles, and Willow in the library and gets caught by Principal Flutie who tells her she cannot leave during school hours.
When Jesse gets staked, the stake goes in closer to his collarbone than his heart.
When Cordelia and her friend are in the computer lab working on an assignment, their dialogue implies it's a database problem. And Cordelia says "goto end," implying they're using a database language. But when we see the screen shot the program is a graphics plotting function in the C programming language.