Continuity mistake: In 3-5 Sight Unseen, we can clearly see Cole turn the air conditioning very cold and open all the windows so that the Prue, Piper and Phoebe can see the invisible demon, and in season 2 when Prue is turned into a man Phoebe asks "did you fix the air conditioning?" But in this episode Phoebe asks Piper why they have never invested in air conditioning.
Visible crew/equipment: In the scene where Prue comes home and finds Andy inside the manor. There is a shot where if you look behind Andy's shoulder you can see half of the body of the director in the background in the observatory room sitting in a director's chair.
Plot hole: In episode 1-2 ("I've Got You Under My Skin"), Alec buys Phoebe a martini at Quake. but then in episode 5-11 ("The Importance of Being Phoebe"), Cole tells Kaya that Phoebe doesn't drink. Then, in episode 5-17 ("Lucky Charmed"), Jason buys Phoebe a "Martini, Dirty" at the end.
Plot hole: The innocent who gets Piper's powers uses them to freeze Piper and Phoebe. But even though Piper and Phoebe no longer have their unique powers, they are still good witches; they were still able to scry, and we have encountered good witches on the show in the past who had no powers at all. And by the rules of magic within the show, good witches do not freeze.
Character mistake: Katya (as Nina) says that Pandora's Box is "a gift the gods gave to Prometheus." But the Box was given to Epimetheus, not Prometheus. Epimetheus ignored the warnings of Prometheus, his brother, and accepted Pandora herself, who bore a box, as a gift from the gods.
Continuity mistake: In the previous episode, Piper tried out for a job as a chef at a restaurant called "L'Opera Ristorante" and was hired by Chef Moore. Then in this episode, she works at a bar and restaurant called "Quake," but she talks about Chef Moore quitting and leaving her in charge of the establishment, so it's not meant to be a different place.
Plot hole: According to the family tree viewed in this episode, Penny "Grams" Halliwell was born on 6/23/1937, and her daughter Patty, the Charmed Ones' mother, was born on 4/5/1950. In addition, Patty's father was born in 1930. So, according to this, Penny gave birth to her daughter at age 12, while married to a 20 year old man. That's quite outlandish, to say the least.
Continuity mistake: You'll notice in some episodes (like "Coyote Piper") that when the sisters look out of the attic window, they can see Prescott Street below, indicating that the attic window is on the front of the house. But if you look at the size and shape of this window, you'll see that there is no window like this on the outside front of the house. In addition, in "Sin Francisco," Phoebe looks out the attic window and sees the front porch from a side view. There's no structure on that side of the house to begin with.
Continuity mistake: When Paige follows Phoebe into the kitchen and is trying to convince her that she is telling the truth, Phoebe's right earring is missing in the shots showing both women, but it is there when the shot changes to close ups of Phoebe. It is an awfully large earring to be hidden by her hair in the two-shot.
Plot hole: When Prue wonders where the cream is, the little container thereof slides along the table to her. Then the cream drains from the container and burbles up through her coffee. However, that's completely discontinuous with how Prue's power ever worked at any other time in the next three years. The cream should have needed to leap out of the container and into the coffee, simply traveling physically across space.
Continuity mistake: Paige asks how The Source was previously vanquished, but she was there both times: when the original Source was vanquished, and again when they vanquished Cole. Also Phoebe want actually there for the Final vanquish of Cole, but was taken back by Cupid as if it was her memory.