Many of the events in the characters' dreams seem to predict events in later episodes. Mild spoilers may follow:
Willow's dream - Tara: You don't know everything about me.
This may refer to things that will be revealed in the episode "Family" (5x06). When Buffy rips off Willow's clothes, the outfit she is wearing is exactly the same as the one she wore in the first episode, "Welcome to the Hellmouth" (1x01).
Xander's Dream - Spike is wearing a brown suit, and Giles says that Spike is like a son to him. This could presage the episode "Tabula Rasa" (6x08), in which Spike wears a brown suit and believes that he's Giles's son, Randy.
Anya: I've been thinking about getting back into vengeance. This may predict a season six and seven storyline in which we explore more of Anya's history as a vengeance demon.
Buffy's dream - Buffy sees her mother in the wall. On the DVD Commentary, Joss mentions that this is a metaphorical hint about Joyce's storyline in season five. The staging of this scene may also refer back to the episode "School Hard" (2x03) in which Buffy talked to Joyce through a hole in a door.
Buffy: (she looks at the clock, which reads 7:30) It's so late.
Tara: Oh ... that clock's completely wrong.
These numbers were mentioned in the episode "Graduation Day (2)" (3x22). At that time they foretold that there were 730 days until a major event. That would mean that there is about a year left, so the "time" is, in fact, wrong.
Buffy: Faith and I just made that bed. A reference to Buffy's vision/dream in the episode "This Year's Girl" (4x15).
Tara: Be back before dawn. This very clearly refers to a major plotline in season five.