Continuity mistake: In "Becoming Part 2" At the end when Spike chokes Drusilla unconscious, he picks her up, one of her hands is resting on her stomach and the other is hanging to her side. It cuts to a shot of Spike looking at Angel and Buffy fighting then to Spike leaving with his back facing the camera. You can see that the hand resting on Drusilla's stomach moved to Spike's shoulder.
Factual error: When Angelus is torturing Giles in this episode he is seen with Giles' glasses, and he cleans them by breathing on the glass and wiping with a cloth. Vampires don't have breath, as Angel tells Xander in 'Prophecy Girl' from season one - even if he can force some air out of his body, it wouldn't be warm, moist air, which is needed for condensation to clean glasses with.
Plot hole: In 'Becoming, part 2' Spike decides he doesn't want to see the world end and makes an alliance with Buffy. Later on, however, he helps Angel get the information he need from Giles to end the world. If he's trying to save the world, why help Angel destroy it even faster? He didn't need to buy Giles any time - he had already convinced Angelus to keep Giles alive for the time being. If he had truly reached breaking point later on Spike could have called in Drusilla then, but as it is he helped Angelus way too early and nearly cost Buffy her life. [Some people disagree at great length, others don't - I haven't seen the episode myself, and the explanation of the mistake and the corrections just make my brain melt. File this under "make up your own mind and just let it go"].