When Harmony first comes in and talks to Cordelia she has her hair in front of her shoulders, but suddenly she has it behind them, it switches back and forth several times without her touching it.
When Angel and Wesley burst in to rescue Cordelia, Harmony alternates between having her arms up or in her lap, depending on the camera angle.
At 9:38 when Wesley lifts up his glasses to look at his phone he is holding his glasses up with his left hand. Then when the angle cuts to Angel he is not holding his glasses. And when it cuts back to Wesley he is holding his glasses again.
Harmony dumps blood on Cordelia's keyboard keys, destroying the computer in a hail of sparks. Keyboards are pretty much waterproof so long as the cable ends remain dry.
When Harmony and Cordelia are on the couch, Harmony's towel is visible in the window behind them as a reflection. Vampires and their clothes have no reflections in the series' continuity.
(at around 1 min) While the Angel Inc. are outside the theater in some shots you can see it raining, while in others it is not. The car is also getting wet in certain shots. And none of the actors are getting wet.
When Cordelia and Harmony are sitting on the couch drinking wine they have their hair wrapped in towels presuming their hair being wet. However, when the shot moves and shows the back of Harmony's head some hair had fallen out of the towel and was completely dry and straight.
The book that Harmony damages is supposedly 'twelve centuries old'. However, a close-up seems to show an antique printed book, which must be less than six centuries old.