Continuity mistake: Paige looks in the Book of Shadows and suggests that the demon they are looking for could be Belthazor, not knowing that Belthazor is Cole's demonic form. But we saw Phoebe making extensive changes to Belthazor's entry in the Book of Shadows in a previous episode, and the changes are not in evidence here.
Plot hole: In this episode Cole says "upper level demons have a human form and they bleed red, not green", but when Cole told Phoebe he was half human he said "how else could I bleed red, even in my demonic form".
Plot hole: After Cole explains he might not be able to regain control after embracing his demonic half, he tells Phoebe she should have the Belthazor vanquish potion ready just in case. But in "Look Who's Barking", Piper tried using that potion on Cole and it didn't work because he had himself magically protected from it.